schl44, Be aware, roads and passes in the Big Horns are fairly steep and curvy. NOT unsafe! But, use common sense. Believe the highway signs, and if you have engine/exhaust/jake brake.... use it! Save the brakes in case you need them!
On the Big Horn Basin side.....
Much to see and do in area: Near Shell... Medicine Wheel, dinosaur tracks in stream (almost always dry) bottom, beautiful off roading in area (BLM & National Forest). Thermopolis, Wy (give us a wave when you pass by Winchester)......Wyoming Dinosaur Center (ranked as one of the best privately owned dino museums in US) and very nice Hot Springs State Park. Also at Thermopolis... The Wind River Canyon, with rafting and great trout fishing. Meeteetse, Wyoming... Very neat museum, Pitchfork Ranch (many Marlboro commercials filmed here), up the Wood River to Kirwin (an old abandoned mining town). Amelia Earhart was having a cabin built here at the time of here disappearance. To get to Kirwin, you need to go later summer(after snow melt runoff), many river crossings and two track road for several miles.
Then on to Cody.... you've probably heard about it and Yellowstone!
:).
Enjoy your trip and "Happy Trails", memtb