Once mud season is over, the Long Trail north of Mansfield is gorgeous and uncrowded (Belvidere and Laraway are highlights), but loop hikes in Vermont are pretty rare.
In general, I'd say buy yourself a copy of the Green Mountain Club's waterproof Long Trail map, and either the Appalachian Mountain Club's tyvek White Mountains map set or Map Adventures' waterproof White Mountains map. In the Whites, it'll be hard to avoid crowds anywhere, but if you stay away from the AT you'll at least have less crowds, and if you camp away from established campsites you'll be nice and alone.
Also, absolutely must do the Grafton Loop Trail. About a 40 mile loop with very rugged terrain, great views, and few crowds. More info on that here.