Looking for things to do in Mystic CT. Mystic offers family fun, nightlife,shopping,restaurants and more, all on the beautiful scenic shoreline of Connecticut. Come stay the day, the weekend or the week. There is plenty of things to do in Beautiful, Historic, Fun, Mystic CT. What are you waiting for for? Start planning your stay today. There is a long list of things to do in Mystic CT with your family. Mystic seaport will give you the opportunity to amble through our seagoing past.