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Emerald Town
A stereotypical suburban town, though this one borders a body of water. You can get to Holy Summit (go north) or Central City (go east) from here. Places of interest are listed below:

Beach: A fighting spot where you will find Tails for training purposes in Emerl's game.
Building: This is where Rouge has Emerl help her steal a chaos emerald. It is the yellow 3-story building.
Emerald Beach: A fighting spot where you will commonly find Sonic for training purposes. It has a beachline, sand, some grass and boxes in various places to create an upper level during fights.
Tails' House: This is where Tails resides when he is not at his lab. It is shaped like Tails' head.
Tails' Lab: A fighting spot where you will commonly find Tails. On the outside, it is the only building on its block. On the inside, it is a big space with orange tubes to create an upper level during fights. This is also where Emerl can go for Virtual Training during his game.
Central City
A stereotypical city with skyscrapers. You can get to Emerald Town (go west), Holy Summit (go north on the east-side of the city), or Night Babylon (go north on the west-side of the city) from here. Places of interest are listed below:

Amy's Room: The apartment where Amy, Cream, and Cheese reside. This is where you will commonly find Amy for training purposes. It is covered with images of hearts, Amy, Sonic, and chao on the ground or on boxes--shaped as dressers--that create an upper level for fights.
Central Lab: The government lab to which Rouge is given access that she also allowed Tails to use to research the Gizoid. This is where Cream will be for training purposes. It is a big space but it has boxes in the corners to create an upper level during fights (referred to as Library outside Story Mode).
Central Highway: A fighting spot in practically all the episodes. This is where you will commonly find Shadow for training purposes. It has the looks of a "highway" with signs, metal fences, and some boxes to create an upper level during fights (referred to as Battle Highway outside Story Mode).
Crossing: A fighting spot in practically all the episodes.
Office: The place where Rouge received her assignment concerning the Gizoid. It is also a fighting spot in Tails' game.
Sonic Team Building: In Emerl's game, you can input the passwords to unlock the Ground Combo moves of Sonic, Tails, Knuckles, Shadow, Rouge, Amy, Cream, E-102, and Chaos for Emerl to use.
Holy Summit
A mountainous, but mostly grassy, area. You can get to Emerald Town (go south) or Central City (go east) from here. Places of interest are listed below:

Altar: A structure northeast of Knuckles' House and southwest of the Crater.
Bridge: A fighting spot in Tails' game near Knuckles' House.
Crater: A fighting spot only in Emerl's game where you will find Chaos. Unlike all the other fighting locations in the game, this one contains craters to create a lower level, instead of boxes to create an upper level. It is icy-looking with some tracks (referred to as Holy Summit outside Story Mode)
Death Egg: This place is only visible in Emerl's episode after the confrontation at the Altar, and it can be found above the Altar as a dot in the sky. As Eggman's flying fortress with which he plans to conquer the world, this is where the end of the game occurs.
Knuckles' House: This is where Knuckles resides. It is marked by the "Knuckles-head" symbol.
Plains: A fighting spot in Sonic's game.
Ruins: A fighting spot where you will commonly find Knuckles. It is a grassy area with scattered boxes that have images of chao on them (referred to as Chao Ruins outside Story Mode)
Night Babylon
A 24/7 night spot for all clubbers, or those who want to have a good time. You can only get to Central City (go south) from here. Places of interest are listed below:

Bar: A fighting spot in Knuckles' game.
Casino: A story spot in Knuckles' game.
Club "Rouge": A battle club for members only owned by Rouge that is the fighting spot where you will commonly find Rouge for training purposes. It has the look of a pinball/slot machine and has a middle circular area and four rectangular boxes to create an upper level during fights.
Computer: A story spot inside Gimme Shelter in Cream's game and a fighting spot in Shadow's game.
Depot: A fighting spot inside Gimme Shelter where you will commonly find E-102 for training purposes. A rather long rectangular area that looks entirely to be made of metal with almost as much upper level as ground due to the rectangular boxes (referred to as Metal Depot outside Story Mode).
Duct: A fighting spot inside Gimme Shelter in Cream's game. It is the only way out of Gimme Shelter for Cream & Emerl.
Gimme Shelter: Eggman's base with a recognizable Eggman design.
Hotel: A fighting spot in Knuckles' game.
Laboratory: A fighting spot inside Gimme Shelter in Cream's game.
Signboard: A fighting spot in Amy's game.
Theater: A fighting spot in Knuckles' game.
Workshop: A fighting spot inside Gimme Shelter in Cream's game. This is where Eggman makes his robots and also contains the key used for Cream's & Emerl's escape.
Extra Locations
These places are only available outside Story Mode:

Colosseum: A dark area that is lit via the outlines on the ground and the rectangular boxes that give the area some form of higher ground.
Green Hill: In an acknowledgement to Sonic 1, a small part of the level is used as a fighting area.
  

Info
Only the necessary battles within each episode are listed. Most of the training and all optional battles are excluded. Some battles will contain more than one fight, usually a 5 KO followed by a 10 KO. The fights become more difficult as the game goes on as the computer becomes "smarter."
Episode #1: Sonic
Battle #1: At Tails' House, play as Sonic and fight Shadow.
Battle #2: At Emerald Beach, play as Sonic and fight Rouge.
Battle #3: At Tails' Lab, play as Sonic and fight Phi. Return to Tails' Lab after the fight.
Battle #4: At Tails' Lab, play as Sonic and fight Tails & Emerl.
Battle #5: At Emerald Beach, play as Sonic and fight Tails & Emerl.
Battle #6: At Tails' House, play as Emerl and fight Phi.
Battle #7: At the Plains, play as Sonic and fight E-102. Tails & Emerl will help.
Battle #8: At Knuckles' House, play as Emerl and fight Knuckles.
Episode #2: Tails
Battle #1: At Emerald Beach, play as Tails and fight Sonic & Emerl. Go to Central Lab in Central City. After being rejected at Central Lab, go to the Crossing.
Battle #2: At the Crossing, play as Tails and fight Rouge. Emerl will help.
Battle #3: At Central Lab, play as Tails and fight Guard Robo. Emerl will help.
Battle #4: At Crossing, play as Tails and fight Guard Robo. Emerl will help.
Battle #5: At Central Highway, play as Tails and fight Shadow. Emerl will help.
Battle #6: At the Office, play as Tails and fight Guard Robo. Emerl will help.
Battle #7: At Knuckles' House, play as Emerl and fight Knuckles.
Battle #8: At the Bridge, play as Tails and fight E-102. Knuckles & Emerl will help.
Episode #3: Rouge
Battle #1: At Central Highway, play as Rouge and fight Phi #1.
Battle #2: At Emerald Beach, play as Rouge and fight Amy. Emerl will help Amy, not you.
Battle #3: At the Crossing, play as Rouge and fight E-102. Emerl will help you.
Battle #4: At Club "Rouge," play as Rouge and fight Amy. Emerl will help you.
Battle #5: At Club "Rouge," you will play as Emerl and go through three training missions. 1) You need to beat a Guard Robo 5 times under a time limit. 2) You need to avoid being hit by Rouge under a time limit--this is the possible hard part depending on what skill cards you have obtained by this point and/or your ability to defend. If running around and your ability to defend aren't very good, Rouge will give you plenty of openings to attack her. If you cause her to start flying (such as by using an upper attack to send her into the air), that will buy you some time. Avoid her overhead attacks by never staying underneath where she is flying/hovering. 3) You need to KO Rouge 5 times before she KOs you once.
Battle #6: At the Crossing, play as Rouge and fight Amy. Emerl will help you. Sonic will help Amy (in the 10 KO fight only).
Battle #7: At the Building, play as Rouge and fight Sonic.
Battle #8: Same place, play as Rouge and fight Sonic, Tails, & Knuckles.
Episode #4: Knuckles
Battle #1: At Tails' Lab, play as Emerl and fight Knuckles.
Battle #2: At the Crossing, play as Knuckles and fight E-102. Emerl will help.
Battle #3: At the Bar, play as Knuckles and fight Guard Robo. Emerl will help. Go to the Casino.
Battle #4: At the Theater, play as Knuckles and fight Guard Robo.
Battle #5: At the Hotel, play as Knuckles and fight Guard Robo.
Battle #6: At Club "Rouge," play as Emerl and fight Rouge.
Battle #7: Phi attack a store clerk, play as Knuckles and fight Phi. Emerl will help.
Battle #8: At Emerald Beach, play as Emerl and fight Knuckles.
Battle #9: Same spot, play as Knuckles and fight Phi #4. Emerl will help.
Battle #10: At the Crossing, play as Knuckles and fight Phi #5. Emerl will help.
Battle #11: At Gimme Shelter, play as Emerl and fight E-102.
Episode #5: Amy
Battle #1: At Beach, play as Amy and fight Phi. Emerl will help you.
Battle #2: At Amy's Room, play as Emerl and fight Amy.
Battle #3: At Amy's Room, play as Emerl and fight Amy & Cream.
Battle #4: At Amy's Room, play as Emerl and fight Amy & Cream.
Battle #5: At the Crossing, play as Amy and fight E-102. Emerl will help you.
Battle #6: At the Signboard, play as Amy and fight Phi. Emerl will help you.
Battle #7: At Club "Rouge," play as Amy and fight Rouge. Emerl will help you.
Battle #8: Same place, play as Emerl and beat Rouge without using a special attack.
Episode #6: Cream
Battle #1: At the Workshop, play as Emerl and fight Guard Robo.
Battle #2: At the Laboratory, play as Emerl and fight Phi. Cream will not fight.
Battle #3: At the Workshop, play as Emerl and fight Phi #13 & Phi #14. Cream will not fight.
Battle #4: At the Duct, play as Cream and fight E-102. Emerl will not fight.
Battle #5: At the Depot, play as Cream and fight Emerl.
Battle #6: At the Depot, play as Cream and fight Emerl.
Battle #7: At the Depot, play as Cream and fight Emerl.
Battle #8: At the Duct, play as Cream and fight E-102. Emerl will help you.
Episode #7: Shadow
Battle #1: At the Computer, play as Shadow and fight Guard Robo. Rouge will help you.
Battle #2: At the Crossing, play as Shadow and fight E-102. Emerl will help you.
Battle #3: At the Computer, play as Shadow and fight Emerl.
Battles #4-9: Play as Emerl and fight Sonic (Emerald Beach), Tails (Tails' Lab), Knuckles (Ruins), Rouge (Club "Rouge"), Amy (Amy's Room), & Cream (Central Lab) in any order.
Battle #10: At Central Highway, play as Emerl and fight Shadow.
Battle #11: At Central Highway, play as Emerl and fight Shadow & Sonic.
Episode #8: Emerl
Battle #1: At the Death Egg, play as Emerl and fight Eggman. Tips: If you have trouble against Eggman, be patient as the best time to attack is after he drops the bomb that will explode (so avoid the bomb) and comes down to the ground momentarily. Also, if you get hit by the missiles, just run away as soon as you can and recover your HP. There are some spots that Eggman will never go toward so recharge in those areas before attempting to attack him again.
Battle #2: At the Death Egg, play as Sonic and fight Emerl.
  

Info
These journal entries will be unlocked after you beat the episode that displays the particular journal entry after you have beaten the entire game once. You can only view the entries after beating the particular episode that corresponds to it. In other words, no option will ever appear allowing you to read the entries anytime you want.
Journal #1 (Sonic)
...I have uncovered a most interesting specimen from the warehouse. I believe it is some sort of puppet or robot made by an ancient people. At first, I didn't think anything of it, but when I was experimenting on "Chaos Emeralds," it began to move. This suggests the possibility that even the ancient civilizations could harness the power of the "Chaos Emeralds." When I was researching various papers related to the "Chaos Emeralds" and this robot, I discovered that there was a possibility that this robot was something incredible. I don't want to get ahead of myself, but this robot may be the cause of the destruction of the Fourth Great Civilization. I'm not sure I believe it just yet, though.
Journal #2 (Tails)
...I am no longer able to ignore the possibility that this robot did in fact destroy the Fourth Great Civilization. I have discovered a stone tablet that explains as much. According to the tablet, "When the figure falls from the heavens, and the Stone of the Gods is joined, all that exists will become one again." Though it is difficult to believe, this robot has been watching my movements, and mimicking all that I do. I was amazed by my scans of this being. Surprisingly, reams and reams of data scrolled and caused my most powerful computer to crash. More intriguing was that the data was all about melee combat and weapons of that age. Eventually, if this being is ever restored to its former state, it will put all that data to use, and recreate all the weaponry and combat abilities that it once had... And that's not all. If my guesses are correct, it will also have the ability to absorb modern weaponry as well. What have I done? I have uncovered a horrible weapon...
Journal #3 (Rouge)
I now understand why this being was named "Gizoid." In the ancient tongue, it means "everything." According to the stone tablet, if the Gizoid establishes a "Link" with someone, the Gizoid will swear loyalty to that person. Perhaps it still lacks "Chaos Emerald" energy, but it has been saying the word "Link" to me in broken tones. It went on to explain: "Show me your true strength, and I shall obey. I am all things, and all shall belong to me." So, as it suggested, I brought before it my collection of model guns, and fired them all. Then, suddenly, it said, "I shall follow your every command, and never leave your side." And since then, it refuses to listen to anyone but me. While it still is a fearsome weapon of destruction, while it remains under my control, at least it won't be used for evil. However, if someone with evil intentions ever forms a "Link" with the Gizoid... I don't even want to think about what will happen. I must research how one can re-establish a "Link" with the Gizoid...
Journal #4 (Knuckles)
The upper echelon is going crazy. Perhaps, they aim to freeze Project "Shadow." Soon, the ultimate life form, "Shadow" will be completed... The application to my granddaughter is also imminent. I cannot just let them stop my study at this point. Because I am the only one who can save my granddaughter's life.
Journal #5 (Amy)
...The higher ups are threatening to shut down this research facility. I had no choice but to hand them the Gizoid to buy more time for my research. I tried to be careful and commanded it to never absorb any dangerous technologies. However, I have heard that other researchers have been making the Gizoid absorb weapons. Apparently, the way to cause the Gizoid to form a new "Link" is to show it power that surpasses that of its former master. While this poses immense danger, I cannot risk losing Maria.
Journal #6 (Cream)
...My worst fears have come true. The Gizoid has absorbed enough weaponry and technology that it has started to go out of control. The resulting rampage resulted in the destruction of most of the "Ark." ...I have deciphered the rest of the stone tablet. It says, "When the Gizoid had learned all that it could, it became a god of wrath, and all was destroyed." The researchers somehow managed to subdue the Gizoid and sealed it away. Luckily, it only had one "Chaos Emerald" installed. If it were to have all 7 Emeralds installed, it might destroy the whole planet. The Gizoid is too much of a liability. I tried destroying its core, but nothing I did worked. I understand too little of the technology that built him. My best hope is to try and reprogram its AI into a free-willed, emotions-based AI...
Journal #7 (Shadow)
...I have heard there was an accident at the research facility. ... ... ... Everything... Everything is gone. My own Maria's name was among the list of casualities. My beloved granddaughter... They tell me her parting words were, "Bring hope to humanity." I have decided that the keyword to activate the Gizoid's free-willed emotions-based AI program will be those very words. "Bring hope to humanity." My poor, poor Maria...
Journal #8 (Emerl)
...A heritage of the past I dug out, "Gizoid"... And the ultimate life form I created by my own hands, Shadow... I equipped both weapons with "heart." If all powers are not what is to be obtained for oneself, but what is to be born from hearts that yearn for someone, I believe all conflicts should cease to exist. Please... If there is anyone listening to my prayers... Bring hope to humanity.