Salt Beach Campground on the Puget Sound side, just west of Port Angeles is a great campground.
The best place for whale watching is probably La Push, a tiny little Quileute village, on the Pacific side of the Olympics. There is a RV Park there that is right on the water. The beach is rocky and and filled with drift wood but was the only place we have ever seen whales.
And as your driving in the area make sure you stop at Ruby Beach, no camping but have your camera ready.
And even though its a dry campground, at least spend one night at the HOH Rain forest. There are tree sections and one has sites right along the river and the other two are under canopies of trees.