Just down the street from the Harpoon Brewery, this place has been open since 1917 and is home to some of the freshest fish you can get. Definitely get the chowder, which is a mish-mosh of whatever they caught that day.
I've gotten the broiled fish or fried fish plate which are all good. It's inexpensive ($8-$12) and excellent food. It's not the nicest decor, but you can get over that.