Sonic Adventure 2Edit
The city in Sonic Adventure 2 is unnamed, but said by many to be San Francisco or Station Square. In the "Dark" story cutscene, Dr. Robotnik reads a news article about how Tails had stopped a bomb from going off in Station Square - a feat performed in Sonic Adventure. The first Hero cutscene states that it takes place "above the capital city", and in Shadow the Hedgehog, GUN soldiers and Doom's Eye refer to Central City as the capital. This concludes that the city in Sonic Adventure 2 is most likely Central City.
Central City appears as an overworld in Sonic Battle. In it, there's an apartment where Amy Rose and Cream the Rabbit live, a skyscraper with a library and a famous database, and a highway called Battle Highway. Tails goes to here to find out more about Emerl. Another part of Central City named "Night Babylon" also appears, as a casino district where Rouge owns her own club and Dr. Eggman has one of his numerous bases.
Shadow the HedgehogEdit
Central City makes its latest appearance in Shadow the Hedgehog. The first city appearing in the game is named Westopolis, but if Shadow helps Eggman light five lanterns in his Cryptic Castle base, Shadow goes to the Central City stage. In it, GUN tries to fight off the invading Black Arms aliens that are trying to destroy the city. The Hero Mission is to help Knuckles the Echidna capture twenty bombs, and the Dark Mission is to help Black Doom detonate five giant bombs. No matter which mission you choose, you have a time limit of 8 minutes. Failure to meet this deadline will result in Shadow losing, one life (presumably) the city being destroyed, and the level being restarted. Shadow the Hedgehog reveals that the President of the "United Federation" nation lives in Central City in a variant of the White House. It is destroyed by the Eclipse Cannon after clearing the Dark Mission of The ARK stage, so whether or not to destroy the city is up to the player. Central City also appears in Expert Mode, where Espio the Chameleon challenges Shadow.