For jazz the two "big" clubs are Regattabar (at Charles Hotel in Cambridge)
http://www.regattabarjazz.com and Scullers (at Double Tree hotel in Boston)
http://scullersjazz.com.
Ryles at Inman Sq. in Cambridge
http://www.ryles.com and Wally's on Mass. Ave. in Boston
http://wallyscafe.com have jazz a few nights a week. Then there's the Zeitgiest in Cambridge which mostly books avant garde stuff
http://www.zeitgeist-gallery.org.
There are various brunches, jam sessions, etc. in the area though most are in the suburbs (will you have a car?).
For gig listings try the Boston Phoenix
http://www.thephoenix.com
As far as the overall music scene here it's pretty good except for the money

There's outlets for almost everything (except C&W)...rock, blues, jazz, folk, reggae, Latin, classical. I'm currently working in bands playing French Celtic music, zydeco, blues and jazz. I can't think of many cities where I could do that

I'm part time and working as much as I want, recently I've been doing 4-5 gigs a week!