There is an RV park in Cle Elum at the exit for Hansen Ponds. Not sure if they take short term visitors. You have to exit at the first Cle Elum exit and turn right at the second Chevron station in town. Follow the road back up over I-90 and right after you cross I-90 turn left. They used to have rental sites on the north side of the river right on the water. Right now these spots would be under about eight inches of fast, brown water.
If i recall correctly isnt there a steep, rugged road that shoots off the side of the hwy down to the river? If memory serves its right before the second bridge you cross heading out of cle elum. Doesnt look like much but its pretty cool down at the bottom and right on the river.
I have not camped there but it looks like plenty of other people have.