Kansas to West Yellowstone

As with an Alaskan trip..... drive on the top half of your tank and you'll have no problem. The roads are good for RVers except if you're thinking of taking 22 west to Victor, Idaho to W. Yellowstone... don't do it. It's very steep. Instead, from I-80 at Rock Springs, take 191 to Hwy 89 and Alpine, Wyoming, then take 26 west to Idaho Falls and then north. It's almost flat. Or... go through Jackson/Grand Teton Nat'l Park (you ARE going to visit it, aren't you?) and through Yellowstone to W. Yellowstone. This will be a slow drive though - traffic so plan to spend time in Grand Teton before onward to Yellowstone. In the Tetons there are two campgrounds with no hookups and each has 300 non-reservable sites. Get there before 2pm and you'll get a site. They are Gros Ventre and Colter Bay. Check out the park's web site. The Tetons are gorgeous.

https://www.nps.gov/grte/index.htm

https://www.nps.gov/yell/planyourvisit/index.htm