Good suggestions. I second the North End restaurants. You'll find Italian restaurants there that rival any in the US.
I'd also consider the USS Constitution or a Celtics game. The Patriots play an hour south of Boston (and about 5 minutes from my house).
One of my favorite things to do in Boston, and hella inexpensive, was to catch a Northeastern University hockey game. World class college talent in a tiny arena for only a few bucks a seat.
Faneuil Hall is a great place to eat, too. One of the best all around spots in Boston, great food, great shops. One of the oldest restaurants in the US is there.