We stopped by the Mystic Seaport on a Saturday during Oysterfest and had a great time. The last time we were here, 25 years ago, we had 3 kids under the age of 12 with us. This time it was only us and one of our dogs. Mystic in general, is very dog friendly if anyone is interested in bring a pet, and the nearby Hampton Inn is an excellent place to stay also.
it takes a couple of hours to walk through all the exhibits of old maritime boats and things, so pick a day that's not rainy. We also went on a small boat tour of the harbor which was very nice and reasonably priced ($4 a person!). Everyone at the seaport was very nice and the oysters were excellent.