Free!
I stayed in the Bridger Teton National Forest off Buffalo Valley Road to be close to the Moran entrance of Grand Teton National Park. There was a large pullout that had a couple of 'sites' below. The view of the Grand Tetons from this spot is gorgeous. It overlooks the valley and the Buffalo Fork River. It's a quite road and peaceful. I had elk around most nights and could hear the sandhill cranes calling down below. This, like most national forest sites, is primitive. There is no fire rings up top and no restrooms. However, it is free!
Month of VisitJune