Where can you go hiking deep in the woods?

Where are all the places you can hiking deep in the woods? What states and cities in the USA have places like that? Is it california or the pacific northwest? Where?
 
we have plenty of state and national parks and forests where you can hike.

on the east coast there is the appalachian trail which runs from georgia to maine and I think even into Canada. plus there are many side trails and state and national parks along the way.

I believe there is a trail system in the rocky mountains similar to the appalachian trail. plus there are many national parks like sequoia, yosemite and yellowstone.
 
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