Try Firehole Canyon in the Ashley Forest. It is in the southwest corner of the state. It is about 20 miles south of Rock Springs. Very cool place.
Here is a shot of it.

Try Gros Ventre
http://www.jacksonholewy.net/park_campg ... ground.phpNice camp ground, on the south end of the Teton park and close to Jackson Hole if you want to visit there. Not well known but worth a visit is a small gravel road with some very cool barns on it. If you are on the road that takes you to the entrance to Gros Ventre , keep going North about 1/2 to 1 mile and on the left is a gravel road . It's called Mormon Road. It has this Barn and several other cool old buildings on it. This is the most Photographed barn in WY.
http://www.themoultonbarn.com/ Go at sunrise for a picture like this.

When you leave Yellowstone take the North east way out and drive the Beartooth Highway into Red Lodge MT. A beautiful drive of about 67 miles, up to an elevation of almost 11K FT.
Well worth the trip. If you are going as far west as the Bighorn MTS. I can give you a few more places.
This will be a great trip. I don't know if Slowcowboy will get his Walk the Winds gathering going this year, but it's located in Pinedale WY. Halfway between Firehole canyon and the Tetons.