[Roll for shoes][1] 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.

  [1]: https://rpg.stackexchange.com/questions/tagged/roll-for-shoes