Some listed as private, allow access on a limited basis.  Worth a call, by you or your pro.

If you're in VT, try Green Mountain National, or Vermont National.  If you can get your pro to make a call, try to get on Quechee or Country Club of Vermont.  Otherwise the mountain courses, Stowe, Okemo are a good take too.  A nice day if you're near Rutland area, is play one of those in the morning and take a ride across the boarder in NY and play either Saratoga National or Sagamore, about 45-50min. away.  Well worth it.  The ones in bold are either public or open for a fee at certain times.

In New Hampshire,  Portsmouth CC if near the Seacoast, or Wentworth by the Sea if your pro can call.  The Balsams and Mt. Washington if you're up North.  

Maine, again the mountain courses, Sugarloaf is nice Sunday River better.  The Legends in York if down south, also  Harris Golf (check their website) owns several nice old courses, Donald Ross,  and the like too.  

Mass, well so many of the best are private, so you'd need your pro to make a call (take a look at Golf Digests top in State, you can't go wrong with any of them, but don't get your hopes up too much).  The ones not listed currently as Top 100 in the Country, most all used to be at one point.   Public, try Red Tail in Devens, worth the C-note. Taconic out west, especially in the fall, and Crumpin Fox if you get there early.  The Ranch, and Orchards in the southwest too.   If you head for the Cape, there are a lot of Town owned that are reasonable and better in the spring and fall when not so crowded.  

RI, again most private, but you can get Newport National which is nice, but Newport CC is better, lots of history, (1st open, Tiger Am, etc.), and Metacomet should be an easy call, Wannamoisett too.  RI CC, home of Brad Faxon worth a call.  

CT, Yale is tops, but you can play Lake of Isles at Fox Woods, one side is "resort" the other private, both nice, you may get lucky.  Fox Hopyard is the sister to Crumpin Fox in Mass., nice take.  I've been lucky enough over the years to play these and none will disappoint.    If your pro can make some calls, you'll owe him.  But you're better off in the fall or spring when the play isn't at it's peak.  Good luck

Hi Pete:

I am a member at Foxboro CC, a semi private course, and am partial to the course.  One fun place that I have played is Kettle Brook in Paxton, Mass.  It is out near Worcester so it probably wont lose the snow until June.  Check out the layout on line.

Mark

In addition to some of the other's mentioned, there's some awesome tracks in Northern New England as well.  

Casper Kill in Upstate NY is a great course.  

Mt. Anthony in VT is a fun one.

The Ledges in Maine

Peabody Meadows

Trull Brook

Portsmouth Country Club (NH)

I live North of Boston and belong to a club that's a solid tack, let me know if you're headed this way, we're always looking for a 4th.

Now if we can only get this freaking snow to melt 

http://www.titleist.com/teamtitleist/team-titleist/f/9/t/3812.aspx

There's a pretty good list here.  I posted this and got a good response when I first moved to the bay state