There are any number of ways to see the USA. An RV road trip is one way you might want to consider.
Americans love their road trips.... and our foreign friends seem to like them pretty well too when they visit. Much of the U.S. is easier to see by road than by using buses or trains.
A rental car has usually been our vehicle of choice when we take road trips far from home, but recreational vehicles are also an option. There are plenty of places that rent RVs for a week or a month.
You may find these recreational vehicles called RVs or motor homes. Outside of the U.S. they are often called caravans. Whatever you call them, they are self-contained accommodations on wheels complete with beds, kitchen, toilet and shower.
Until recently we had never considered an RV road trip for a number of reasons. The top two reasons are that RVs don't get good gas milage, and if you don't own one, they are a little expensive to rent. Then we had the opportunity to take an RV road trip with friends, and we saw the positive side of this kind of travel.
In the U.S RVs come in sizes from a little bigger than van size to really large, so you have to consider that you will be driving a vehicle bigger than what you're used to.... maybe lots bigger.
We discovered that this was not quite as limiting as we thought. Most attractions and stores have parking lots that accommodate even the largest "rig". You have to watch height limitations at gas stations and road underpasses, and narrow lanes can be intimidating... but once you're used to it, you will travel just as quickly in an RV as you will in a car.
Stopping for the night is not a problem.