Stay here! I arrived (very) late, around 10:30pm or so after a long day in Tetons/Yellowstone. I drove down and most spots were taken. I stayed in a little pull out on the side of a cliff. I could hear water running, but it was dark so I couldn't see. I woke up to the most beautiful view ever. It was incredible. The creek running at night was lovely to listen to. A cool trailhead is on this road as well. The sites looked awesome as I drive away, they were just all full. Definitely keep this in your pocket if you're in the area. The road was pretty tame. I'm in an outback and it was easy. 2wd I'm sure would be fine. Also the stars were INCREDIBLE.

https://www.fs.usda.gov/Internet/FSE_DOCUMENTS/stelprd3833681.pdf