I second most of the above recs and add a few of my own:

The wonderful candle_beck's THE LAND OF THE BLIND
http://archiveofourown.org/works/218151

also spn_J2fan's THE GOOD PLACE (made me cry)
http://archiveofourown.org/works/881304/chapters/1696643

kellwyntar's VETERANS OF THE PSYCHIC WARS (J2)
http://psychicwar.livejournal.com/3181.html

You've probably read leonidaslion - if not, her SUITE!verse is dark and twisted - not post-apocalyptic, but right spang in the middle of the Apocalypse, with Sam as the Boy King and Dean as his hostage. Seriously, very dark.
http://archiveofourown.org/series/6436

aaaannnnddddd - to lighten up that last one, you should read fleshflutter's THE INCESTUOUS COURTSHIP OF THE ANTICHRIST'S BRIDE - not exactly dystopian but very funny - and hey, it has actual zombies!
http://fleshflutter.livejournal.com/100930.html

oh, and tabaqui's COMES TO DUST
http://archiveofourown.org/works/671615

*Sorry to keep adding on - I've got one in my head that I can't remember the title of, very powerful story. Hope I can remember it for you.*