IX would be my choice, but then again, I've only been able to get my own GF to play FFX and X-2, as well as a third of FFVI. Then again, I got her hooked on Metal Gear Solid...take with that what you will.

I would also echo foa's sentiments, about FFIV, especially if you use the DS version, the story is more "friendly" to modern gamers and the difficulty curb could make sure you get some quality time together playing.