Here are a few of my favorite places...
Near Port Angeles - this county campground looks over the Straits of Juan Defuca - awesome views: Salt Creek Recreation Area
There are some very cool gun embankments here from WWII - good history lessons here.
Cape Disappointment State Park, Southwest of Ilwaco. beaches, clamming, pristine 1200 acre park.
White River Campground, Mt. Rainier National Park - hiking, great wildlife, etc. Get reservations early!
There's great camping in the cascades - you might check out the Roslyn area (avoid winter here - it's vicious). Northern Exposure was filmed here and the area is beautiful.
Wander further east to Leavenworth. Ye olde Bavarian village but very lovely and great camping and rafting there along icicle creek.