I think there is the Greyhound bus system which covers the whole country. This could be a solution to travel easily among various states, without the trouble of being dropped at 100 km from the closest motel...Thank you for your suggestions.
Definitely do NOT hitch hike, as we have all heard of the horror stories that come with it,
and like others have said, it's illegal in places, as well.
The best way to do what you want is to get an unlimited bus pass (Greyhound) for a time period. That way you can go where you want any where in the continental US.