OK, how about US 34 across NE. Definitely not as fast as I-80 as you have to slow for every town. Stop at
Pioneer Village for the night, taking some time to see the museum. Never camped there, but the museum does give good insight to life on the plains.
There's also a small CG in McCook right off the highway. Run by the city. No fee, donation requested. Flush toilets, 30/50 amp, showers. Not bad for the price, but only seven sites, three day limit.
Google Maps does show it's only a two hour flight from Denver to Davenport! Just look down at it instead of a ground level view.
