Boston to Sharon to Providence to New Haven
Jodie, don't know if you are staying in Boston a few days? or what time of day you are departing Boston, but the CH raved Neptune Oyster in the North End- has a pretty famous lobster roll. Some CHs have talked about getting lobster rolls to go at J Hook(seafood store) on the waterfront near So. Station. Island Creek Oyster Bar and Neptune Oyster are the 2 seafood spots most consistently raved on this board. I like both of them very much, though they are opposite experiences. Do a search and many threads will come up.
Don't know when your trip is, but soft shell crabs are on a lot of menus here; they are quite a delicacy if you haven't had them before.
This is a great spot for another part of your trip:
The Sea Swirl on Rt. 1 in Mystic is pretty good. We mostly get the fried clam (whole belly). Maybe a notch below the Essex/Ipswich places but not a big notch.
I see they have a lobster roll (never tried it) but they don't do whole lobsters. Mostly fried stuff.
Outdoors only (picnic tables under a large tent).