SEE-Science Center, Peterborough
Address 300 Bedford St., Manchester, NH Map, Tel 603.669.0400 Call, Website
This is a fantastic hands-on science museum for kids, in a managable size. There is a section aimed at crawling babies, and stuff right up through teens. The only issue is that it's two floors, so it can be tough with several kids of different ages and only one adult.
Also here is an enormous model of the town made of legos that you can walk around but not touch.
The museum is a little hard to find in a big old mill building; look for the signs.
There has also been a dino exibit on another floor here, with robotic lifesize dinos that turn their heads (and scared the pants off my 3 year old at the time). I understand it is currently closed for renovation.