The Whaling Museum is my number one favorite thing to do with my kids when it is raining.
The reason I like the Whaling Museum so much is they have a kids room, where kids of any age can be free. There are many educational activities if you have a little precocious one, or tiny ones can simply walk around or ready books in the cozy barrel in the corner.
Kids can touch anything in the room and the items are geared toward children. It is a diamond in the rough on a cloudy vacation day.
In fact – all of the Historical Association properties are great to visit on a rainy day – you can view all of the properties here.