Oh, if you want a tip as a gamer girlfriend: Dragon Age II is terrible
But seriously - finding a girl here who tolerates gaming is incredibly hard enough and I've had my share of arguments about games in the past. I think a lot of it is narrow-mindedness - where it's ok to read a book but not to play a game with an interactive story you wish to unfold. Or it's okay to lazy about on the couch watching a dull acting flick but not okay to be the one playing a online FPS where your brain is constantly engaged.
So good luck on breaking the mould! If I can give you any advice : don't stick to the typical girl choices for games which are:
World of Warcraft
Object hunting games
Those are really the mainstream fringes of gaming. Instead, try the classic adventure games, try a few RPGs, even dabble in an action game or two or a good old strategy game!