Mystic Seaport is a lot of fun. You could easily spend an entire day there There are several different parts to visit including going on a whaling boat and inside a lighthouse. Throughout the day there are events such as harpooning and rope making. It is on the expensive side and the price can quickly add up if you want to take a boat ride, visit the planetarium, or participate in craft making.
The lighthouse is on UCONN campus and has a nice area to walk around with free parking. I don't think you are allowed to go inside so its just nice to look at. There is a nice area around where you can look out at the water, but nothing to actually do.