This site will tell you about each forest service campground:
http://www.forestcamping.com/dow/rockymtn/bigh.htm
we looked at almost every campground across the bighorns on 16 and then drove up and looked at 3 or 4 on 14.
Across 16 we found Sitting Bull and South Fork to be nice campgrounds. Also up by the lake (Meadow Lake?)is a campground that will hold you ok. There is a dump station up near the top of the pass.
The town of Ten Sleep has an rv park on the west side. it's very shady, has full hookups and a nice owner. Bathroom is so so, but not too bad.
Up off 14 highway, near Burgess Junction is Sibley Lake, with elec hookups on a lake. A few miles east is another campground that's real nice looking. And there's a third one we didn't look at that is west of Burgess Junction. There is a dump station at Burgess Junction. Do not take 14 A going up or down. It is a very tough climb or descent...very tough.
If you feel you can hike it, do go and take a look at the Medicine Wheel, but you have to hike the last mile and it's uphill. There is a bathroom at the top. If you're handicapped, they let you drive up there.
Bon Voyage.