The only places I can recommend are the places I've personally visited/lived (in no particular order):

1. Burlington, Vermont. It's a fair-sized city, but not big by any means. It's right on beautiful Lake Champlain, and is a very pretty town. Lots of good places to eat. Church Street is a fun promenade, but it's full of hippie whackos.

2. Hanover, NH. Love this place. The home of Dartmouth, right on the border of New Hampshire and Vermont. Lots of covered bridges in the area, lots of little New England towns to visit. It's close to the Joseph Smith Birthplace Memorial, which I would definitely recommend.

3. Lake Winnipesaukee. I have personally never been here, but everything I've heard has been great.

4. Mid-Coast, Maine. Portland, Freeport or Brunswick. This whole area has to be one of the best places in the world. The coast line is incredibly beautiful (drive out to Bailey Island to see what I'm talking about). Go visit some lighthouses (Portland Headlight, Pemaquid Point). Eat a lobster roll at Red's Eats in Wiscasset. Drive up to Bar Harbor if you get a chance.

Oh man... typing this is making me want to go back. New England (and Maine in particular) is a beautiful, beautiful place.