Wait a minute -- I just remembered a BLM campground right on the beach -- Mattole Beach Campground. Very beautiful -- almost like boondocking.
The only catch is that it is a really difficult drive to get there --- long and twisty and narrow. Don't take a big rig on this route. A truck pulling a small trailer can do it safely. (I have!)
Here is our blog post on Mattole -- once you open the page, scroll down to July 7: