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. There are RV parks all over the country, and many county, city, and National Parks have spaces for recreational vehicles, so there is no problem finding a place to park for the night. There are even some large store chains that allow you to spend the night in their parking lots... though that is not really a very scenic option.
You need to learn a few things about full hook-ups and partial hook-ups for the night, but your rental agent will give you the basics you need... and people you meet in RV parks are friendly and helpful. There are plenty of websites specifically about the RV experience and RV road trips where you can find lots of information if you're interested in trying it once.
One nice thing about this kind of travel is that once you've got your RV set up, you have your clothes and food with you all the time. No need to go finding restaurants.... though you could if you didn't want to cook. You will meet lots of friendly travelers.... people in RV parks seem to like to talk to each other and share their experiences.
You might even find that it doesn't cost you any more than a rental car and hotels or motels along the road, and you might find an RV road trip a whole new kind of adventure that you like.