Roll for shoes is the system I have used in this situation. It's very easy for you to game-master and it's very easy for muggles and kids to pick up and play without feeling like they're immersing themselves in some baroque super-geeky subculture. My kids enjoy it and we can pick it up and play at any time with almost no prep.
I enjoy board games and even some of the new D&D board games. But it sure isn't role-playing.
