Of all the worlds that captured my imagination in regards to post apocalyptic story, the Original Gamma World
by TSR (First Edition) really did it for me. Seeing a map of the U.S. with the coastline "slightly" changed due to something happening and then wondering what the major cities are like was something I could sit on the couch and just let my imagination run with.
There is a sort of draw that keeps the player wondering and interested by obscuring the nature of what happened (what caused the everything to go to hell) as to use it as a prize for the player to find out. If there is a way to do that...it's like crack, you Just HAVE to continue because you HAVE to know the how and why the world got all screwed up.