It depends on how you are flying in. If you are flying in to new york, from heathro then flying out the same way, maybe you can stop in NYC for a few days, see the sites, like the statue of liberty, and ellis island. Also you could take in a show, but order tickets 6 mos ahead so you can get good seats. If you fly in through Los Angeles then there are a lot of great places to go on a short layover. I'm going to bet you are flying in through NY, then changing to fly to whyoming. America is a really big country, with a lots to see. Hope this gave you some ideas.
This is a good idea. I would try to fly in through one city, such as NY, and out through another like DC, and spend a few days in each.