I quite like lingering dates, say meet up in the afternoon for a hot beverage then if you get on well you can go for dinner or a movie or a stroll or something.
Or a casual drink is always good.
This!
My current girlfriend and I had our first date by just meeting for coffee at a bookstore. Granted, this was in lower Manhattan, so anything we'd want to do was close by. We wound up not having any coffee. Instead, we bounced around the city all day, going into various shops, wandering through Central Park, and then saw a show on Broadway. It was an awesome date.
I think the best way to go about it is to go in with something casual planned, but be willing to throw the plans away to do whatever comes to mind.
I don't recommend a first date consisting of just a movie or anything like that, though. Hard to get to know each other if you can't talk, right?
The advice others gave about doing something you are both interested in is also good. Just don't get totally committed to whatever you come up with--being fluid is a plus!