Great Yellowstone Basecamp just a few minutes from the entrance.
There are a ton of awesome campsites along snake river with about 2 sites per pull-off. Actually, most of these are a little bit more than a mere pull-off. On gmaps, the sites seem to continue all the way on into Idaho. The one we took, we almost missed because as usual, we arrived at nightfall and we turned onto a dark uncertain path with a lone RV parked off to one side, and sure enough, the was an empty space right there waiting for us, complete with trash, toilet, and even a bear box. Each pull-off has 1 toilet and 1 trash, but has a firepit, table, and bear box for each designated camping spot. The river seemed perfect for fishing. I hope to come back one day.