Might want to consider fueling options once you get out to Nebraska, assuming you'll stay on US 20. From Valentine through Chadron and on to Lusk WY and Casper WY, it's a whole big empty there. Last time I was through Lusk, for example, there was only one gas station open. Granted it's been a few years but I can't imagine much changing there. Valentine and Chadron are good sized towns by Nebraska standards. Some of the other "towns" that show up on the maps are little more than a collection of a few houses, with very limited services to be found.
If you're going to take I-80 through Nebraska and on to Cheyenne WY, then north on I-25 to Casper, the same advice still stands about fueling, particularly once you get to Ogallala. There's Big Springs, Sidney and Kimball to plan on for fuel, and Pine Bluffs just across the state line in WY for fuel. There's more places to stop but it's still a good idea to do a bit of planning.
Heading north on I-25 to Casper from Cheyenne, there's Chugwater, Wheatland, Glendoe and Douglas for fuel. WY fuel prices are always among the lowest in the country!
Hope you have a good, safe trip out this way!