Well, I like going to restaurants, but since it will be one of your first times with this girl I suggest you don't go do an expensive restaurant. I would choose something cheap like a Chinese restaurant but with all the fancy politeness like a waiter coming to get your order and stuff like that.
Oh and don't make it sound like you've planned a romantic dinner. Else she probably thinks you're paying as well. Just ask her: did you planned somewhere to eat tonight else we can grab a meal at "Chinese restaurant's name"... or I don't feel like cooking tonight, if you want you can join me, I'm going to "Chinese restaurant's name"...
After dinner I always go to a lounge bar or somewhere cosy and get my dessert or coffee there, not in restaurant. Just to change venue and so I can continue the romantic conversation in an even more romantic environment.
A future idea might be: going out for a weekend (city-trip) but this is more for people who are already into a relationship.
ZACK
PS: I you know any fun activities to do with a girl please tell me cause I can only think of clichés like movie, going out, ... maybe I'll start a topic of my own.