Hi Jean,
Please don't miss Captain Scott's lobster dock in Groton, its a little bit out of the way and the lines tend to be long, but for very good reason. The thing to order is the hot lobster roll... If you've never had one, I am totally jealous of the way your mind is about to be blown.

My other recommendation is breakfast at Kitchen Little in Mystic. "Little" refers to the size of the place, NOT the portions.
Kate