Depends on how far west in Nebraska you're interested in, but we liked Ft Kearny State Rec Area (you'd need advance res's for a weekend night, though) - electric hookups at the sites, nice shade. A really big rig might have a problem fitting in most sites, though.
Ft Kearny State Historic Park (different park) is nearby & interesting if you're into history.
We actually liked the Cheyenne KOA (in case you find you can get to eastern Wyoming on the day you were aiming for western Nebraska). Big rigs may have to unhitch to fit in the pull-thru sites, and the CG is covered in river rock (round stones about the size of golf balls) so a bit difficult for those with mobility issues, but it's very clean and the road & train noise isn't bad at all.
Haven't stayed there, but Cabela's in Sidney, Nebraska has a fairly large CG, with space for big rigs and hookups, behind their flagship store there. Walk to restaurants as well as to shopping in Cabela's itself. It gets good reviews.
We're just learning some places in Idaho, but have so far enjoyed Massacre Rocks State Park near American Falls (electric-water hookups) - big rigs won't find many sites to fit in, and the lower loop will be far less noisy; Bruneau Dunes State Park - about 20 miles or more off the interstate but quiet & peaceful (busy on weekends but a great star show then!), electric hookups; Castle Rocks State Park by the City of Rocks - off the beaten path but within 45 miles of the interstate in 2 directions, elec-water sites in pinon pines, great view, some sites will accommodate big rigs. Village of Trees RV "Resort" just east of Burley is nice - not as shady as it sounds like, but fairly large grassy sites, FHUs, and along the Snake River; older but clean facilities. Friends have seen the Mountain Home RV Park and said it was very nice; we haven't been there yet.
I do not recommend the Boise-Meridian KOA. Tight spaces, an RV parking lot. Clean, but not where I'd choose to stay again. Our local KOA (Pocatello) is making improvements, and many sites have some shade - awfully nice this time of year!