I work on the corner of Washington and Causeway, which is practically across the street from the Garden. So I am fortunate to get to go out to lunch and business dinners in the area often. The Boston Beer Works and the Fours are right across from the Garden and have solid bar food.
Trattoria la Famiglia is on Salem Street about 5 min walk from the Garden and has tremendous Italian food and obscene portions for a reasonable price ($13-$18). My favorite Italian place in the North End is Ar Tu on Hanover Street, little more expensive ($18-30) but tremendous.
There is a great seafood place called Posiodens on Salem, top notch raw bar. And that place makes me think of pizza, because Ernesto's is right next store and that is my lunch joint. Pushcart further down Salem and the Original Regina's are can't go wrong choices. Stay away from Half-Time on Causeway.
Lastly, I'd be remiss to not mention Bolle Nolle on Hanover, it's a sandwich shop and it's probably not open but I have to plug my old friends. They make a great Pastrami sandwich!