Lots of galleries and exhibitions are open in the evening, and are always great date night idea.
They're interesting and exciting and suggesting going to one proves that you're more than just a pretty face.
When it comes to choosing the right kind of exhibition, why not suggest something that you really want to go to?
That way they can learn a bit more about you, and you can impress with your knowledge on the topic (no showing off though, that's not so sexy).
If there's nothing you particularly want to go to, ask them what they like. It doesn't look like you've got no ideas, it just shows what a kind, caring and very dateable person you are.