Upstate NY, Adirondacks or Catskills.
Jersey Pine barrens
None of those is in New England. Not a one.
Guest: being among the 13 original colonies and instigators of the Revolution, New England is one of the most populous regions in the US.
Try areas in the White Mountains of NH in the area of Lincoln, Ossipee, and North Conway and Tamworth area. Green Mountains of Vermont. 100 mile Wilderness in Maine. Perhaps Acadia National Park area, also in Maine. That's another favorite area for me, since Bar Harbor is nearby.
Berkshires of western Mass can be nice, and actually tie in to
@Dave in AZ Adirondack suggestion, as well as Green Mountains.
Check Gaia GPS app and the DeLorme Gazetteer paper book maps the are state specific. Pick up the AMC trail maps for the area as well. Pour over them at the dining room table and you can come up with some peaceful places.
Again, "away from people" in New England wont be the same as in Montana or as I imagine as in Utah, but you can get far enough away to not feel the crunch, but close enough to pick up some gear or provisions on a near whim.