If you have some spare coin I would highly recommend going to the Bruins game on the 8th. It is the season opener vs. the Flyers. Hard to find a better way to get a feel for the local vibe in Boston than a Bruins game. You will probably need to buy tickets online.
Otherwise, be sure to get some seafood. Legal Seafood is always a good choice with several locations in the area, and there are countless other local joints that know how to serve it up. Atlantic Fish was great, but quite pricy. A few others I just can't recall right now. Pretty hard to go wrong in Boston.
If you like touristy stuff, walking the Liberty Trail is a fun experience, especially with cool fall weather.
If you prefer sitting on your ass, get a Duck Boat tour. They are right in front of the Prudential Center.
I'd get a beer with you, but I'm a few hundred miles north in Maine and I'm not supposed to be drinking beer right now.
Enjoy New England!