Rafter J or Custer State Park (Game Lodge campground) for Rushmore visit
highway 16 west to I 90 to Buffalo and 16 on west across the Bighorns...several national forest campgrounds along that route...
small rv park in Ten Sleep on the west side of town...
Ponderosa RV park in Cody is a good one if you're planning to do the Bill Cody Museum. Otherwise, Buffalo Bill State Park about 7 miles and 15 miles west of Cody. And further out, there are a couple national forest campgrounds with elec. Wapiti and Rex Hale...if you want to get closer to Yellowstone's entrance gate.
In Yellowstone, Fishing Bridge in the only one with full hookups.
Bridge Bay is about 2 miles away with water and dump station.
Madison is on the west side of the park with water and dump.
Reservations NOW for any of these parks except the one in Ten Sleep or national forest campgrounds.