My favourite is the Portuguese Holy Ghost Society's Lenten Fish Fry. Stonington is home of the last fishing fleet in CT, so the fish is really fresh and they use an ultralight batter that you can taste the fish through. As Stonington is also famous for sea scallops, I recommend the fish & scallop combo
Some other favourites for the rest of the year (mostly during the summer season) are Costello's in Noank, Evelyn's in Tiverton, Cove Fish market in Mystic and Sea Swirl in Mystic. Unfortunately most of these shacks are not 100% dependable as it really depends on who's in the kitchen and who made that batch of batter.
Further north along the coast my favourite in the elbow of the Cape is Sesuit Harbour Cafe. It has amazing water views and is located behind the Dennis Yacht Club.
Just got word that the Stonington Portuguese Holy Ghost Society's Fall Fish Fry will be starting Sept 28th

It'll be held every Friday from the 28th through the Friday before Thanksgiving and then again for Lent. I highly recommend the Fish and Scallop Combo. In the same area, Costello's is closed for the season, but Abbott's is still open on weekends until Columbus Day weekend, Sea Swirl tentatively too on the same schedule. Sadly I can't recommend Cove anymore as the 2x I tried it this season has been extremely disappointing