Check out these threads:
"Any tournaments in the Boston area?"
http://forums.azbilliards.com/showthread.php?t=136121
"A few questions from a new player in MA"
http://forums.azbilliards.com/showthread.php?t=155952
"Weekend tournaments near Boston"
http://forums.azbilliards.com/showthread.php?t=158170
Google Maps is a good start, but some listings won't be up to date.
I would second the recommendation to visit World Class Billiards in Peabody (4 carom tables + plenty of 9-footers) and Country Club in Chelmsford. If you venture farther north on 3 you'll find Maxamillians in Tyngsboro, MA and Boston Billiards in Nashua, NH.
http://www.yelp.com/biz/world-class-billiard-peabody
http://www.countryclubusa.com/
http://www.maxamillians.com/
http://www.bostonbilliardclub.com/
There are places to play in Boston that you can access using the T or the bus system, but if you go to Felt (near Boston Common) or Flat Top Johnny's (Kendall Square).
http://www.feltclubboston.com/
http://flattopjohnnys.com/
Note: The pool room in Sacco's Bowl Haven is gone, though judging from the crowd on Super Bowl Sunday (7 Feb 2010) bowling is still popular. A restaurant will be opening up in the pool room.
http://www.saccosbowlhaven.com/
I heard that the administrator for Onepocket.org lives in New Hampshire, so you might check out that site's forum if you're looking for someone to play One Pocket:
http://www.onepocket.org/
If you play 3-cushion then you can find tournaments at World Class in Peabody and at Cue and Cushion in Hooksett, NH near Manchester. There's also a hardly used 3-cushion table in Keene, NH.
If you're looking outside of Boston you might also scan through the list on the following site, but it hasn't been updated and a number of rooms are closed:
http://www.billiardscoop.com/billiard-rooms.asp?s=ma
Closed: all Boston Billiards locations except for the two in Nashua,NH and Worcester, MA; Good Time Emporium in Somerville; and Renaissance in Quincy.