http://jameshooklobster.com/index.php?main_page=product_info&products_id=16174
Chowder fest champion
Keep in mind, this is a small fish market, not a restaurant. It's smelly and seating is minimal. You usually take it to go, or people eat them on outdoor seating on a beautiful summer day.
They also have amazing lobster roll.
If you want a nice sit-down restaurant, Neptune Oyster seems to be getting all the rave.
http://neptuneoyster.com/
Barking Crab is also good, albeit touristy. Great seafood.
No-Name restaurant is good too on Seaport.
Union Oyster House is also good, supposedly the oldest restaurant in US (1826). Good seafood.
What I've listed are all great seafood.
McCormick & Schmick is a chain, but on Tuesdays, they have dollar oysters.. which are local (New England). Absolutely amazing. Google and call them (was it Wed?).
If you are into Asian food, Peach Farm in Chinatown has great seafood. They do a good ginger scallion wok-seared lobster.. MMMMMMMMMMMMM.
Shabu-Zen is a fav hot pot place of my GF & me. Great seafood selection there also.
Boston also has pretty good pizza. Uppercrust on Beacon Hill is good. Same for Pizzeria Regina.
Boston is a small walking city, so Chinatown, Beacon Hill, and Little Italy are all within 15 min walk (or just 1-4 stops on T).