Without more to go on, I'm not sure what to recommend. What
kind of post-apocalyptic game are you looking for?
My favorite is Twilight 2000, which is more "during the apocalypse" than post-apocalyptic -- but the mood is unbeatable. Instead of being post-collapse, the setting is mid-collapse; most of the PCs are assumed to be in the (dissolving) armed forces. There was some funkier stuff introduce later on, but no cybernetics that I can remember.
Palladium's After the Bomb game is anthropomorphic animals in an entertaining post-apoc environment. The system is about as clunky as any other Pallaidum game, but the character creation process makes up for all of its flaws.
Deadlands: Hell on Earth seems to be pretty popular. I can't stand the mechanics (of the original system), but the setting is neat.
There's always GURPS -- grab the core book, Compendium I, and one or two others (High Tech or Ultra Tech for cyberware, Thundarr the Barbarian for a specific setting, etc.) and you can bend it to your will.
Avoid Rifts at all costs, except perhaps as a source of cool artwork.
