First date ideas for shy girl, in the coldddd winter?

We met online. We've both talked a lot and texted a lot for a week or two and know each decently well personality wise. She is a little shy however, and said she might be a little shy in person at first just because she finds me super attractive.

She says she's a hopeless romantic and anything would be nice for a first date. She wants the first date to be a surprise and just doesn't want me to spoil what its going to be. So she told Chinese food is her favorite food way early on in our talking. I was thinking of taking her to a PF Chang's nearby because I've also never been. But I want to add to that. Its very cold here. It will probably be 20 degrees out the entire day. Should I walk around the mall with her? Take her to a movie? I think a movie is too generic to go along with the dinner (although she is a hopeless romantic, but still).

Any ideas? I don't want to spend a ton of money of course. She knows I'm a college kid and don't have a ton. I'll pay for the dinner OF COURSE. But what else should I do? And should it be before or after the dinner?

She's 19 and I'm 22.