The best first date is one that could be construed as either a date or just hanging out depending on how it goes.
Very this. Ala's ice skating idea was pretty good. The main point is to do something that's not so cliche, but also something that's not so "omg this is a date!" Keep the romanticism to a minimum, make a lot of eye contact (but don't stare), and smile alot. This will keep her relaxed and more prone to opening up, and the date as a whole will go better. Also, think of some lightly probing questions ahead of time to get her talking - ask her about where she grew up, what she thought of high school, if she likes cooking, etc. Try not to resort to the stereotypical small talk questions like "what kind of music do you like?" or other predictable departures. Be funny but in the natural course of the conversation (if you're forcing it she'll know).
Your ultimate goal is to get her to talk as much as possible, with you saying just enough to keep her interest. This will simultaneously let you get to know her pretty well, and it will keep her intrigued because she won't know as much about you. This makes her more interested in a second date so she can continue to learn more about you.
Finally, try to be ambiguous with some of the things you say. This way you can drop subtle hints that you like her without being wide open, whilst still allowing you a way out in case she doesn't respond. This will also continue to make her ask questions in her head about what you mean, and thus increases her intrigue even further.
I know, it sounds like a lot. This is a first date after all, so keep it simple. Just be a bit creative so you stand out from other guys she may have dated.