You should tell us what the constraints are on your 22 days. Will you have a car? Will you have a budget for plane flights? Must-see in the US, from the point of view of someone who has been mostly everywhere: For the outdoors -- Niagara, the Grand Canyon, Yellowstone, Zion/Bryce, Yosemite, the Pacific Coast drive, and a whole bunch more. Unfortunately most of those are far away from each other and way west. The east has the Smokies/Shenandoah, nice history, some charming cities and a fair amount of decent coastline. Also Acadia and the Everglades but they are very out of the way. For cities -- beyond NYC, you should make it to Chicago because it's the quintessential American city, to Detroit for the sake of hubski, and to the various west coast cities if possible. If you find yourself in the south, go to New Orleans and Austin. Note that August is the worst month to go to the last two. It also depends what you're into.