The Adirondacks in NYS.
You want to live like Thoreau. He had wealthy friends on whom to depend. So go where you can access friends, when they are needed.
l check out maggie valley or any surrounding city in north carolina ............... i vist there often i have family there .......... or colorodo ...... i use to live in colo................. but i moved cause im a beach city person
Smoky Mountains, North Carolina.....
I hear Vermont is nice, anywhere in the north east is good
Serious answer: the Wind River Mountain range, most has not been seen by any but native Indians.
The Ozark Mountains are beautiful, and the cost of living is cheap...it's backwards though and very low tech in general, but very beautiful and some very friendly people. For the most part I grew up there...had to move though as it didn't feel like home to me.
The Appalachians are even more beautiful, but I didn't spend much time there so don't know much more than what I saw on my way through...but I can tell you there's at least three amazingly great people in Kernersville NC there that saved my butt when my van broke down :-)
colorado has some decent mountains, i'm not sure how you plan on getting food and essentials, and making it through the winter...but there are nice mountains
far away from people? then, are you prepared to live off the grid? many people think they are but find out they aren't.
Southwest Colorado, has a lot of little towns in the Mts. that are very remote but not far from civilization. The woods look like scenes from Bonanza...
I want to stay in America? What's up with the Himalayas?
The White Mountans in Arizona are nice.