A film sounds like a good idea. And don't worry about blushing. It's not awkward. It's adorable.
Consider, also, some conversational topics. Not to have a script but to have a few go-to's. Politics and religion are too heavy for a first date. The weather should be an absolute last resort, and sports a second-to-last resort unless you know she's a sports fan. Work and/or school should be pretty low on your list, too.
A few ideas of what to talk about (in no particular order):
- Books you have recently read
- Concerts you have recently attended
- Do you cook or bake? Maybe you can bring up something interesting you made, or even a funny story about a kitchen disaster
- What you wanted to be when you grew up, back when you were, say, five years old
- Places you would love to visit if money were no object, and why
- What you think will be invented next/what's going to be the next big thing?
- Whether you think there's life on other planets (I'm a geek so I like this one, but your mileage may vary)
- The first job you ever had
- Your favorite film of all time
- Which ten songs would you take with you to a desert island if you had to stay there forever and could only listen to those ten songs?
- What's the best/scariest ghost story you have ever heard?
I realize it's easy to see some or even all of these topics as being lame, but they are all safe and inoffensive, and they don't have any right or wrong answers. And don't forget to listen more than you talk!
It'll be great. Don't worry.