Off of the politics, I think a road trip is probably the best thing you can do to get a feel for america as a whole simply because of the variety. Go online and get a big stack of tourist destinations from all over the place, then string a good number of them together, and go.
Personally I really recommend Albuquerque, New Mexico as one destination.
It's the polar opposite of Scotland, as far as the land goes. Instead of constant rain and cool temperatures, you have desert heat and air so dry your sweat evaporates almost instantly (making the heat rather pleasant). Where Scotland has green grass and rolling hills, New Mexico has a neutral palette of reds and tans and has the best sunsets to grace my eyes. Also, they have proper South-Western food to which Taco Bell doesn't hold so much as a smoldering twig.