Muppet, I'm a little late to this thread, but let me add to the Mystic/Groton/Stonington love. You won't regret spending time there.
You might also consider off-season Cape Cod. Especially Hyannis Port and the other Barnstable villages. Or venture further to the Lower and Outer Cape for some places which will feel quite similar to Cornwall. Hell, there's even a Truro to visit. Provincetown will knock your socks off, even during off-season.
Also, a few days on
Block Island is pure heaven.