Abbott's can be really inconsistent when its busy. Generally it's solid, but I've had a few meals there that were borderline inedible.
It was a shame that Skippers Dock closed in Stonington. They had the best lobster dinner (with sides) in CT. The owner just got tired of running it by herself. Something else moved in there, but I haven't tried it or even researched what it is.
Try the Venus de Milo in Somerset, MA (near the RI border) for baked stuffed lobster. The place looks like something out of "My Big, Fat, Greek Wedding" but they excel at that particular meal (made with Ritz crackers, of course)
Generally a restaurant can't do anything with a lobster (on it's own, not prepared as part of a recipe) that you can't do yourself at home. You steam it, crack it open, and eat it. Pretty straight forward . . .