Ifyou're playing the 'questions' game, heh, I could think of a lot. Just ask her questions about what you're into, to find out if you two have similar interests, etc.
What are you genuinely interested in knowing about her? I think that should be the basis of your questions. Or, at least that's what I'd do, not that I have any experience in relationships. So take that with a grain of salt.
music is definitely one of the very first things to get to know about another person. at least, that's how i see it. but it's really all about what you're into. see if she's into the same stuff.