Mystic is a lovely little place with a beautiful waterside setting, and the Mystic Seaport museum is well worth a visit and is a good day out.
It's a collection of old ships and houses with a series of small museums, each telling a different aspect of American seafaring - boatbuilding, whaling, early settlers etc. It's all well-laid out in a spacious setting but it's not far to walk between each - think of a little village by the sea which is exactly what it is. I loved the old houses most - furnished as they would have been back in the 1800s or earlier, with good attention to detail.
The whole place was not at all crowded and we went on a Saturday in June.
Some boat trips are available. There is also a small art gallery, but the works are expensive and most of it was not open when I went.
The cafe/bakehouse had no gluten-free cakes or cookies, so I could only have tea.
Elsewhere in Mystic there is a little shopping village with various shops selling gifts and so forth and a couple of cafes and restaurants.