One of the recommendations I received before moving to Boston was to have cocktails at Russell House Tavern. They do have great drinks, but now most of the time, I come here for the $1 oyster special, which starts at 11pm til closing.
A lot of places don't serve the freshest oysters when they do $1 oysters, but I've had great experiences with Russell House Tavern, and I've come 3-4 times. The first time they had Island Creek oysters. I also had Moon Shoal oysters once. Not only the types, but these are also fresh and cleaned properly (unlike the $0.50 I had at Red House which were not that fresh and weren't even really cleaned well).
The cocktails I've enjoyed included the Howling Winds ($12): Ansac cognac, yellow chartreuse, cinnamon syrup, lemon, butterfly absinthe, bitters, and Battle of Trafalgar (pictured below, $10): Pimm's no 1, elderflower liqueur, Batavia arrack, honey, lime.
There was also Burma Nights ($13): Bombay East Gin, P.F. Dry Curacao, Orange Flower & Jasmine Waters, Lemongrass, Regans No. 6.
I've tried the other dishes which tend to be good and reasonably priced like the Steamed Moosabec mussels, Spanish chorizo, fried garbanzo, white wine, grilled Fondi bread ($10)
Smoked lamb belly meatballs with taleggio, roasted tomato, crispy sage ($9)
They also have lobster tails for $8 each! Served with saffron aioli, it's a great place to get a taste of affordable lobster.
Torchon of Foie Gras, Boston brown bread, sour pickled cherries ($14)
14 JFK St
Cambridge, MA 0213