What people should visit in the united states are the national park. It is really something that we don't have in france, because there they have many vast national park that are magnificent. I went during my expatriation to the grand Canyon and Yosemite. And it was impressive, in those park you have the impresion that you are nothing compared to the nature. There are only the lodge for habitation and you are pretty much away from the civilization.
The grand canyon was beautiful with its red rocks and the hights of this monument of the nature. I did something called skywalk, where you are walking on a bridge that is like a window and you can see what is beneath you, it was really impressive
Yosemite was for me as impressive as the grand canyon with its waterfall and big mountains.