If you have a high clearance, check out ponderosa park. On Casper MT, I drove there in a Volvo 940, it's possible, but difficult. Otherwise, check out Crimson Dawn Park, also on Casper Mountain. While I haven't been there, google Ferris Dunes, also in Wyoming. It is extremely isolated, however, and a truck or ATV would be essential, less you hike in some 15 miles, but the photos I've seen of the dune field are spectacular. The BLM runs a nice campground on Muddy Mountain just beyond Casper Mountain, the valley between the two is very beautiful rangeland with red soil speckled with mature juniper growth and has good public access.
Seminoe Pass via Magical Mile is an excellent detour, and Seminoe Reservoir itself offers some unique opportunities. Fremont Canyon and Alcova are good if you want to stay close to the highway. Both are accessible with 2WD and located in South Central WY, between Casper and Rawlings.
Beartooth Pass in northern WY, southern, MT is also an excellent choice if you have an extra day, IMO the area is better than Yellowstone itself. Lots of opportunities in the sun valley and the pass itself travels well above treeline. you'll end up in the charmingly unpretentious village of red lodge, MT. Outside red lodge there is also the Silver Run trail, a good medium difficulty trail which leads to a couple high altitude lakes. Keep in mind though there is still a lot of snow in the mountains here.
