we took Rt2 going east from Alliance about 10 years ago. There was very little traffic, two lane, no rest areas, and a few, small towns, bypassed by the highway. So if you need a bathroom, you have to go down into the town to find a place to stop. Other than that, no complaints.
We've also done the 83 south from Valentine to North Platte, and again, no problems.
I've always wanted to stop at the National Forest campground, but haven't yet.
Chadron is a great little state campground. If you like visiting archaeology digs, the Hudson Meng Bison Kill site (do a search)is interesting and so is the Fort Robinson state park. It has a couple good little museums and a film of the history of the fort. There is, or was, a little chicken stand on the highway to the fort... with BROASTED Chicken. Very good and the only broasted chicken place I've seen since the 1960s.
Chadron has a free museum on the south side of town with a whole lot of stuff from the early pioneers to that area. And another museum on the east side with Fur Trapping history.
If you are going to be there around mid June, the Sioux put on a PowWow fair at Ft. Robinson.