Because real life is just like the movies:
The US is WAY too big to hike. You'll have to drive some of it.
If you do happen to hike a trail, you do need a gun. That's not me being a jackass like the above video... the Appalachian Trail is supposed to be spectacular but bears who're acclimated to humans, and Appalachian inbred methheads are both fairly common.
If you enjoy the mega death shits, potentially getting kidnapped by the drug cartels, or getting kidnapped by overzealous rednecks who don't understand that just because you're obviously foreign does not mean that you're trying to sneak into the country, I highly recommend Mexico. If you want the good parts of Mexico without the death shits, death Mexicans, and drunk border patrol vigilantes, I recommend visiting Texas. All the Mexicans who're worth a damn are in Texas these days anyway. Besides, you can't really come to the US and not visit Texas. I recommend Dallas, although Austin is big on tourism. Avoid Houston. While you're in the neighborhood, I'd swing back east and visit New Orleans. It really is the best place in the US.
If you were ever curious what hell was like, I'd make a stop in New York City. Ultra-high population density combined with ultra-high douchebag population density and a laughably high cost of living makes it miserable. Although it's about the only place you can still go to an Italian restaurant and the hostess is known simply as "mama" and she keeps a shotgun behind the counter. And there's something to be said for seeing the mob, I think.
I hate to say it, but as you head west from there...there's nothing good to see until Chicago unless you head south. If you're in the area in August, I'd stop by Indianapolis for GenCon, which is the largest gaming convention in the US (and if I had to guess, probably the world). Otherwise... I'd stop by Chicago, then either go to the west coast or head south. Between basically Chicago and California (north of the Mason-Dixon line, at any rate) there's basically nothing of interest, unless you've never seen farms before.