I spent a few days in the area, 4 or 5 maybe. I spent one day at Celebration Park. It was listed as a free CG on the BLM site. They do charge $5. You can camp just out side the gate for free however as I found out the next morning. They are set up kinda strange I think. Notice how my camper door faces the away from the water. That's because the fire pit, picnic table and benches are back against the mountain. You cant get on the other side with a camper or a tent. You could put a tent next to it but not behind it. SO the camper faces away from the water to toward the table and fire pit. Or the other way. No good. I left that site after one day and went Southeast. Idaho puts out a booklet with the scenic drive that shows the way from Kuna, Id to the BOPNCA. The BLM website also lists the other sites as well. Those sites are great and set up correctly. They have flush toilets at Celebration Park and 2 vaults in the other/better area.
The last pictures of the canyon and the dam show the camp site from above and also after I drove down into the canyon you can see the sites along the river. If you go Southeast you'll find many many many free BLM managed free CG. It's all dry camp.