Im down in Fall River and go to the Freetown State Forest a decent amount. It is a huge place with a decent amount of unpaved roads that acquire decent sized ruts and puddles throughout the year. I like it as it isnt too brutal yet you can easily spend an afternoon out there and not be in the same place twice. Check it out on a map and see. I have a couple pics from there when I have been I can post.
You need to define "off-roading". You want to just get a little dirt under your tires for an afternoon, I second Freetown State Forest, just stay on the roads.
To me "off-roading" means (meant) serious rock crawling, and required a purpose built rig, a trailer, and a diesel Excursion for a lot of trips to NH and Western MA.
Do yourself, and others in the sport a little favor though. Where ever you decide to do it, make sure it's LEGAL. Just because your buddies "go there all the time and no one says anything", doesn't mean it's legal. Many people have spent a LOT of time trying legitimize the sport, and all you'll ever hear about is the bad apples, tearing it up in some guys field or something. If you're really serious about getting into wheeling, look for a club. Many have exclusive access to legal land, and you'll meet a bunch of cool new people and friends.
I agree with rblank - gotta be careful where you go. Practicing "pack it in pack it out" is always good too - there are a lot of unmaintained/abandoned town roads around my area that are still legal for public travel, but heavily used for illegal dumping. I've found that I generally get mean mugged by neighbors/local residents once or twice but when they see me go in more than once with an empty bed and come out with a couple junk tires or an old couch or something in the back, they realize I'm clearing stuff out, not leaving more of a mess. Doesn't even cost me anything as I'm 3/4 of a mile from the town dump and they run a free dump day every 3 months.
Are you looking for some trailriding/dirt roads/washouts, hardcore rock crawling, mud, or what? What kind of traction control and recovery equipment do you have, if any? Are you afraid of dents and scratches?