Looks like you're looking for someplace to stay for a night between I-80 and West Yellowstone. We have stayed in the Rock Springs KOA - it's nothing to look at, but has clean facilities and is fine for a night. The federal (NFS) CG below Palisades Dam looks decent - expect some road noise but the scenery is nice. We have not stayed there yet. There are some others in Palisades and Swan Valley that we are definitely considering in the future, though, for short campouts - as suggested, check out those locations on rvparkreviews.com. West Yellowstone has some wonderful CGs; our favorite is Grizzly, since we don't dry camp and need reservations; they should be open by then, but each campground's website should tell you when they open.
An alternate route from Rock Springs to West Yellowstone would be to take US 30 north from I-80 (west of Rock Springs) through Kemmerer WY and Montpelier & Soda Springs ID to I-15, then head north to US 20 in Idaho Falls - take that north to West Yellowstone. Some CGs along that route include the Lyman KOA (if open), Montpelier KOA, Pocatello KOA, and a few NFS CGs in Island Park ID. Some - especially the NFS ones - may not be open yet, but Rock Springs & Pocatello KOAs are open year-round. From anywhere along that route, it will be up to a day's drive to Madison CG. This route is somewhat less scenic than the one through Alpine, but is less likely to have problems with wintry weather over most of it. (Montpelier to Soda Springs may still have snow on occasion.)
Given the parking lot sizes for Mesa Falls, I'm not sure I'd recommend that stop while you've got your rig in tow.