It's a little ironic that the hardcore/casual divide has grown to the point where it's really hard to find a game with crossover appeal. Hell, even among the hardcore there is a lot of steep-learning-curve stuff that scares away people new to them.
Case in point: My ex-wife is a Blizzard fangirl. Her first game was Starcraft, she plays WoW, she plays WC3 on Battle.net, but she is absolutely clueless in any other genre. She knew Rome: Total War was (and is) my favorite game of all-time, so she asked to borrow my copy of it so she could install and play it. I showed her the basic game mechanics and explained the battle screen...and she had Gauls at the gates of Rome within ten turns. Which would've been great if she were playing as Gaul, but she was playing as the Julii!
Also, her lifetime record against me in Rise of Nations was 0-43 (and why didn't I let her win? Because she was the kind of girl who'd rather lose 43 times in a row than know when her man was holding back!)
Edit: So what's my point? It's that getting a non-gamer into gaming is harder than you think, and it might be impossible. Hope you've got a lot of other stuff in common with this girl or your entire relationship might be founded on flawed principles (and trust me, I know where that leads, having ended up married to a girl who had only tangential interests in common with mine---but had stonking great tits and a high sex drive, in case you wondered how it all came together.)