I used to spend a lot of time in Boston for business and have some favorites.
The best Chinese food on the planet is at Xiao Xiao (I'm not sure I'm spelling it correctly, its pronounced Chow Chow) which is in Chinatown. I recommend the sizzling beef and the salted-spicy shrimp in shell.

Fabulous, fresh, yummy food.
I love to go to the Green Dragon (bar) in the North End area. This is on the Freedom Walk and was supposedly the secret hideout of the Founding Fathers. You can go have a beer where Benjamin Franklin did.
Over fairly close to Faniuel Hall is a fantastic Irish bar called the Black Rose. It is also a steak & seafood restaurant, but I've never eaten there. They usually have live Irish folk music at night.
There is a great seafood restaurant on the wharf, which is in one of the Founding Father's wharehouse buildings. It's near the city aquarium. I forget the name and the details, but maybe someone else will remember.
Take the MTA to get around -- the first subway in the US, and one of the very first world-wide. Look for mice on the tracks at the stop, its crawling with them.
Jim