I'm gonna give you my trusted date-plan. Used to work well when I was on the market. It went like this:
I used to take girls up to the roof of the tallest building around here, it's not "that" tall, only 17 floors, but anyways, it was a nice get-away. They rarely changed the lock on their security door, and it was easy to pick open, so I had it all prepared before the night. Then I'd take a blanket(trusty old spots), a bottle of wine and a couple of glasses. Then I'd take her up there and we'd sit/lie there looking at the night sky(or if she felt adventurous, looking over the edge down to the people) and talk. I'd try to impress her with my very rudimentary knowledge of stellar bodies. Sooner or later, a cold wind would start to blow our bodies closer... Well, after that is all up to you.
So that's it, do something semi-adventurous, nothing major. But do something that will leave a mark at least. Personally I'd never recommend the movies or things like that, it's not that special. Plus, movies, come on? That's just a reason NOT to talk to each other. You have to do something that actually involves getting to know the girl! Something personal for you and something new for her.