I could live here.
I stayed here twice around July 4th this year, and couldn't believe the was space available! You can't make reservations, but the ranger at the Quinault Ranger Station told us there were spots available, so it may be worth stopping there to ask if they have any info on space.
The campground has one working bathroom but no sinks or potable water. Sites 1-5 and 17-20 are my favorites because they back up on the river.
There is a beautiful (and freezing) swimming hole behind the campground, and this time of year its bursting with huckleberries :)