My girlfriend and I enjoy places like this and this is will be our very first visit here. Plus, I'm celebrating her birthday as well. Would this be a good place to have a bit fun/romantic for a couple of nerds like us?

I don't know that it would be romantic. It is a children's museum. But you should definitely check out the after hours events. Those are a lot if fun.

Yes. You may want to see what museum After Hours events are happening also (science of beer, etc).

Absolutely. My wife and I are pretty nerdy and we went on lots of great dates here. One of our favorite places!

Yes

If you like nature, there are several areas outside with chairs/benches that overlook bird feeders, the pond, and wildlife. It also has a nice trail around the park. There's a hammock large enough for two, although this us quite popular with kids...I usually see 4-6 kids on there constantly.

Yes, and i suppose the outdoors in the museum would be beautiful in spring