Have you checked the Public Lands site? There are some great camping spots along US-191 - Wyoming Centennial Scenic Byway - south of The Tetons.

Hobach campground is 8 miles south of Hobach Junction, on the western side of the road, right on the Hobach river. Right by the road, but ever so quiet and secluded. There is another about five miles further south, on the east side of the road, also on the Hobach river. Not far after crossing the bridge over the river. A further one can be found at greater altitude - hence, no trees - at Warren Bridge, just south of the bridge on the western side of the road. Tom and Dianne are the camp hosts there, and Tom takes great pride in keeping the place neat and tidy. All these are about $15 per night.

BTW, I would not count on an eight hour drive to Moab. US-191 in Wyoming is an attraction in itself. Don't short change yourself. There's much more than the NPs. Check out the Flaming Gorge / Green River Scenic Byway.

Call in at the BLM office in Pinedale, and have a chat with them there.

Lifey