Central City is one of the planned locations to be in the game. It will be a copied remake stage of the same name from the game Shadow the Hedgehog (once a map of this level is found). As the game takes place years after Shadow's game, the stage of the ruined city will be remade as an Adventure Field/Town Stage of the restored city, with no bombs, aliens, toxic floods, ruined roads or buildings (or fake walls) and not even the dark atmosphere.
The city will be more peaceful and easier to run through with NPCs to talk to, some will give you Missions such as stopping Eggmans robot raids to a task to do in an Action Stage. The city will also be the location for G.U.N. HQ. While the details of reason of this Adventure Field is yet planned for the game, it will be important for the DLC characters story Shadow and Rouge. So far, two Action Stages are planned for this place called Rushing Roulette and West Highway.
As exact layout of the original stage may vary plans, one of the major features to the north is a G.U.N. Headquarters where you can meet the Commander. Another planned place is a gala hall you can enter that will lead to Rushing Roulette. To the very west of the city is West Highway. The exit to Viridian Valley is the suspension bridge/train station to the south.
Actual Action Stages
One scene in mind is you do a mission in Central City's gala or casino and you will have access to the buildings balcony which also is the entrance to the casino theme park stage Rushing Roulette which might be a treasure hunting stage for Knuckles. The stage is named after the potentially lethal game of chance Russian roulette.
The city will have many civilians around the place. Also outside of G.U.N. HQ will be G.U.N. soldiers. Perhaps even possible to enter G.U.N. HQ and have idle chat or receive missions from the commander of G.U.N.
Central City is located in the midwestern part of the Federal Republic of Columbia, in the state of Peoria. In this world, it shares a number of features with Chicago. BearfootTruck hasn't created any fanfics that are set here (yet).
In the custom canon created by MalikTH, Central City is the same city as Station Square, having been rebuilt and renamed after the Perfect Chaos incident. It is the birthplace and current home of Malik the Hedgehog, Frost the Wolf, and Kai the Fox. As a result of being a rebuilt Station Square, it is accompanied by Emerald Coast and the Mystic Ruins.