Mystic for 3 days, for sure. Lots of great food and things to do! Easy to get an uber to the casinos if that’s your thing. On day 4 you can uber to new LOndon easily and take the train to New Haven. Eat some pizza, see Yale, go to the Peabody, stay a few days. Then can go to NYC or Boston from there. These places are touristy from CT standards but not in general. Other nice places along the train lines are Old Saybrook, Kingston RI, and Madison I believe. It’s very hard without a car, each city has something to offer but Ubers can be unreliable here (most won’t drive more than 30min away) and most of the best spots require driving. If you do Mystic also check out Bluff Point in Groton for a nice hike on the water near a tiny regional airport