"The Ruins" is a name given by the Citizens to all the parts of Rapture which haven't begun to be Rebuilt. There you will see the devestation of 'civil war' fighting (and of later conflicts), lack of maintenance, willful destruction, and inhabitation in ways not originally intended.
An interesting feature of the MMORPG would be a visible progress of exploration/repairs/rebuilding happening in Rapture (done by the Players). Because of an integral Auto-Generation system Rapture can expand outward AND inward continuously to allow the Game World to progress without limit. Even old locations would mutate and change as new Assets were added by the other integral element of the game - Player Creation.