One of the most secluded and magical places in the USA is the Kalalau Valley on the island of Kaua'i, It's the basin visible at the base of the sheer cliffs in this 8x10 inch plein-air painting from 2000.
No roads lead to the valley. You reach it by getting a permit and and hiking in along the narrow Na Pali trail, which follows the coast.
The mountain walls rise up almost vertically from the valley. It’s inhabited by wild goats and chickens, and a few campers. At times in its history it’s been the home of a small society of people living entirely off the grid, beyond the reach of law and custom.
Wikipedia on Kalalau Valley
See a photo from the same spot