I live and work in Boston, so I can give you a few tips.
No offense to whoever mentioned it, but skip Cheers, it's a tourist trap, and really awful.
The rest of the recommendations are fairly solid. You might be there around the time of the "Head of the Charles" (
http://www.hocr.org/index2.html) Regatta, but, maybe it's a little too late. That's always really neat. Make sure you go for a walk along the Esplanade along the Charles River. Very beautiful walk.
Check out Cambridge, just a few T stops (the subway) away from Boston. Lots of good used record stores and restaurants catering to vegetarians. Newbury Street is nice for shopping. Go to the Public Garden, and the Common (in Boston). Boston's Chinatown is one of the most authentic C-Town's in the USA. Although, as a vegetarian you may not appreciate the smells and sights (lots of chickens, hanging everywhere).
If you're up for the drive, Walden Pond, just north west of the city is really beautiful.
Providence, RI is a really nice city as well. I currently live about halfway between Boston and Provi, but will be moving soon, but I split my time between the two cities. Provi is even lower key than Boston, a great town.
Check out the Museum of Fine Arts (the museum across from NorthEastern). I used to live across the park from the MFA, in Fenway, which is also a great section of the city. You may just want to swing by Fenway park and see if you can get some tickets to a game when you're there. It's well worth it...great ball park, and the Sox will be well on their way to the World Series by then after having decimated the Yankees in the playoffs (or at least keeping them out of first place). Check out the Brown Sugar Cafe in Fenway. Amazing Thai Food. My apartment's back window faced their kitchen, so I was reminded on a daily basis that I could cook boring food at home or go eat there.
Anyway, I'm babbling on. There's lots to do. Enjoy.