D.H. Lawrence wrote a small book called 'Apocalypse', but that's more of an essay, than an adventure story. It's about religion and all that...
However, if you really want to read a good book with a post-apocalyptic setting and lots more, I can recommend you 'Slapstick or Lonesome No More' by Kurt Vonnegut (Jr.). This is what the cover says:
"Now, as America collapses into anarchic decline, and pin-size Chinamen pollute the atmosphere, President Wilbur Daffodil-II Swain sits in the ruined remnants of the Empire State Building and tells the extraordinary story of his life and times..."
An awesome book. Actually, everything by Vonnegut is pretty awesome.