You don't say when you're going- some campgrounds close for the season soon after Labor Day...
As it happens, I just did the same trip, but in reverse!
I live on the Olympic Peninsula and recently did the 101 from Laytonville, Ca. all the way to Astoria, Oregon.
Having driven the 101 in Washington lots of times, we cut over to the I-5 corridor from there...
The Oregon Coast is simply CRAMMED with campgrounds, most of which will easily accommodate your rig.
The Washington Coast is a different story- big chunks of it are Indian Reservations with little or no "outsider" access.
Kalaloch Campground in the Park is beachfront and near the rain forest.
My favorite spots out there are the (free!) DNR campgrounds along the Hoh River, though.
No amenities, of course, and first-come-first-served, but beautifully situated.
And the Hoh in the fall
is an easy float if you like to do that kind of thing