New Hampshire:
White Mountain National Forest
This page has a guide for a dozen or so short hikes.
Cohos Trail
Remote, great for the experienced backpacker,162 miles in Northern New Hampshire to the Canadian Border. Please check link for updates as permissions become available from private landowners the course of the trail changes. You’ll meet more moose than people and for a 90 mile stretch there are no towns. Towns, by the way have a population of 900 or less. Also shorter day hikes are available along the Trail. Bear country, also moose.
Pemigewasset Wilderness