Another good place to stay overnight along US83 is McCook, Nebraska. It has a very nice campground at Karrer city park that only costs a $5-$10 donation for 50A electric pull-thrus with big shade trees, available potable water, and a dump.
McCook is a neat little town with a hilly downtown, brick streets, and the only Frank Lloyd Wright-designed house in Nebraska. The house is still privately owned, so no tours are possible. The town was begun by the Burlington railroad, but now relies on agriculture, ethanol-production, and oil for its survival.