There are several DNR campsites
in the Western area that are out of the way and lightly used, free with Discover Pass. Not the greatest in terms of scenery, especially the logged out zones on the drive in, but pretty nice once you get there and probably not hard to find a spot. The ones I've checked out on the north coast are either always full (Lyre River) or horribly un-scenic (Sadie Creek).
You probably already know the Makah Reservation has closed their borders, so don't try to go to the northwest tip.
I'm a huge fan of the views and tide pools at Salt Creek Rec Area, but you absolutely have to time the low tide correctly or it's a waste. There's great campsites there, but it looks like the good ones are all reserved for quite a while.
Please report back with anything you find, positive or negative!