When are you coming? A lot of the nicer shoreline activities are pretty seasonal. I'd say Mystic seaport and the Aquarium is one, downtown New Haven for restaurants, bars, normally I'd say museums, but 2 of the 3 are closed for renovations, but the Yale art galley is still open and is free. Of course you have to have New Haven pizza. Pepe's, Sally's and Modern are the big 3. Go to all amd report back with YOUR favorite because it's a very decisive argument.