Definitely make a reservation in peak months. But only if you're going to use it. This was a nice, well maintained campground. Easily accessible to West Yellowstone. Not the closest, but it's tucked away and really pretty.
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
Lovely little spot. After reading reviews I opted for going on FS 838… There were large camp sites. There was a large group in one when I went by, and other sites that could fit maybe 4 or so cars. I sleep in my outback so I found a little spot. The road was pretty rough, some large divits and larger rocks on the road. I drive an outback so I just went slow and it was fine. It evened out around the corner, the but the beginning was rough. Enjoy it! It's a great spot for an over night and seemed to have a ton to do around the area, it was just a stopover for me.
I showed up around 11 pm on a Thursday and found an open spot not too far in. Road, as far as I went, was an easy dirt road. I just set up shop real quick and went to sleep with the sound of the creek running. Woke up to the birds. There were a few spots tucked away it looked like, but the first spot I found (maybe 4-5 spots in?) I took. Not sure what's further back, but I'm sure it's great! There were a few big groups set up, looks like a fun place near Jackson to have as base camp. I didn't have any cell service. No amenities as I could tell, but not too far from civilization, and it's so beautiful.