Can't answer Q on your proposed route. Except we have driven US 20 in WY many times & it was always an easy drive. Haven't been back in some time. Used it from I-25 to Lusk. Might consider dropping over to Smith Falls State Park, a very unique place. Wouldn't expect it in Nebraska.
However, maybe something in this might be of help: In WY: Overnighting Sites & Sights in the
Douglas & Wheatland Area. Includes Guernsey & Fort Laramie Area.
Guernsey State Park -------
Fort Laramie National Historic Site ------
Oregon Trail Ruts and
Register Cliff Off US 20, Fort
Robinson &
Chadron State Parks in the Northwest corner of the Nebraska so seem neat from their websites.
Another neat one near Valentine,
:C Smith Falls State Park. We did an overnight there, as did my son earlier. Neat place. Unique Place. We were traveling US 83. US 20 crosses there as well.
On the border NB/SD there is an Indian Casino at the state line. The Rosebud Sioux Tribe Casino Wacipi. Not far north of Valentine. I believe one can overnight at it. We have never stopped, except for fuel.
More
Nebraska US 83 Sights.
US 26 South of Fort Laramie Area. Goes to Scottsbluff, by Chimney Rock, Ash Hollow & near Lake Ogallala State Rec' Area by Ogallala. Never driven this, but would have liked to.
I-80: North Platte, Nebraska: the
Buffalo Bill Ranch State Historical Park and
Camping; never stopped there, but driven by on US 83; nice looking campground by the river.