I always liked bowling as a first date. It's fun, casual, active (rather than passive), allows some breathing room (like, you're not constantly focused/focusing on the other person; you're doing stuff too), good place to converse. Maybe it's a bit old school, but it's better than dinner 'n a movie.
Otherwise, if she's the outdoorsy type, I'd take her out on a hike (lot of good trails near me), and we'll stop at a nice spot (like a lakeside) and enjoy the picnic lunch I cooked up either the night before or that morning.
I'ma bowling FANATIC but the idea that bowling is a good first date is a myth in my book. You're always standing up and walking away from your date. Unless you're Mr. Smoothe and can swing the "Hey, let me show you how to do that..."
Bowling is a great activity when you want to introduce a larger group.
Best first date? Pool of Thorns concert: