The maritime museum at Mystic Seaport, CT is one of the coolest museums to visit that I have been to, especially with kids! It is a huge outdoor museum that we wandered around for several hours.
There are old wooden boats you can tour and see crew demonstrations and hear sailor songs, which the kids really enjoyed. There are lots of things going on everyday so check the daily schedule when you go.
There is a Children's Museum, Playscape Area, and Discovery Barn for kids. We talked to this really nice old man about his family trade of building and restoring boats by hand and he talked about his grandfather building one of the boats in the Preservation Shipyard.
The recreated 19th century village is really neat and the Museum educators were great with answering questions. I think the kids liked the water front the best though, pretending to captain a 19th century ship.
Even though it was drizzling a little we loved it! I highly recommend spending a day there.