I'm going to echo Umbran. Can you better define 'good'? I've played/run a fair number of such games and a system that is 'good' for one set of expectations is not good for another.
Apocalypse World, Morrow Project, Aftermath (though this one fails the easy to learn part), Post-Apocalyptic Hero, GURPS + source book,, or a FATE variant can be good at the right table with the right expectations and lousy with the wrong ones. If you want to tell a story and waive the details then FATE, and to a lesser extent Hero, or GURPS. If you want the PCs to be AWESOME then Apocalypse World, Hero or GURPS. If you want more scrabbling for survival then Morrow Project or Aftermath and to a lesser extent Hero or GURPS.
If you want a more fanciful world then Gamma World (one of the many very different editions: I'm fond of 1e and 2e), Darwin's World, maybe Desolation (I own it, but have never played it and can't comment too much on its quality), Hero or GURPS.
All Flesh Must be Eaten is good for during apocalypse.