we stayed at the park one night on our way to Glacier NP. in mid Sept. two years ago and had no problem getting a spot. The spot was next to the river with I think with water and elect.I think they had a dump station. It is a nice park with lots of trees , walking paths and a visitor center. Google in Idaho state parks and you will find more info.
If you are coming from Clarkston WA. when you go across the bridge over the Snake River you have to make a Rt. turn at the end of the bridge and work your way down a two lane road to the park, just watch for signs and take it slow and you won't have any trouble. Have a good trip. Jay