Zombies are an ever popular option but I think you're going to want to look into more detail.
Supernatural zombies or sci-fi zombies?
Chapter-based or sandbox?
Is there mechanics to consider to enhance the survival element, or is it a looser rp?
Is character death a factor, to what extent?
This is what i was thinking:
The zombies would just be supernatural, its year 2500 and the U.S. has been nuked. (not gonna go into by who) After the fog of the nuke clears, undead creatures started to appear. People kept getting ate alive by them. A majority sandbox, sometimes there will be chapters, just to inform if the zombies have mutated, another strike on the U.S., etc. Near the beginning there will be power, but after awhile power will be cut off. Limited bullets also, you can be infected by the air. Only if you got a cut or something, better get those cuts covered up quickly! You can die, by the usual, getting shot, from zombies, getting infected, the usual.