Hoo boy, ok lets start North and work around clockwise.

Moran State Park on Orcas Island is very cool, Mt. Constitution is the highest point in the islands and you can see forever. http://www.parks.wa.gov/parks/?selectedpark=Moran Moran is pretty well known, however, so it might be booked.

The San Juan County Park on San Juan Island is kind of a "hidden gem." It's on the shore of Haro Strait and not a lot of people know about it. http://sanjuanco.com/Parks/sanjuan.aspx

If you have a boat or are willing to hire a water taxi, there are dozens of wonderful boat-in campgrounds in the San Juans. I won't go into too much detail on that because I'm thinking maybe you are looking for a car-camping opportunity, but Stuart, Jones, Clark and Sucia would be high on my list of recommended boat-in campsites in the SJIs.

On the mainland, Larabee State Park up in Bellingham is a great one. It's at the foot of the Chuckanut Hills on the shore of Puget Sound, some people say it's the only place where the Cascades touch saltwater. http://www.parks.wa.gov/parks/?selectedpark=Larrabee&subject=all

Also to the North, my cousin swears by the Burlington KOA. I hear Burlington, I think strip malls, but this is out on the Eastern edge by the Skagit River. Apparently it's quite nice. http://www.koa.com/campgrounds/burlington/

Silver Lake is another "hidden gem" off Mt. Baker Highway in Eastern Whatcom County. One of the few places you can rent a boat for cheap, and the trout fishing is top-notch. http://www.co.whatcom.wa.us/parks/silverlake/silverlake.jsp

To the East, if you're willing to cross the North Cascades, the KOA in Winthrop is actually pretty nice. I spent last 4th of July there and enjoyed myself. The trout fishing on nearby Peregrine Lake just might be the best in the entire state. That's pushing past your three hour mark however.

Another great spot in that direction is Lake Osyoos. This is bigtime "hidden gem," I know I am overusing that phrase, but this one is for sure. It's a five hour drive from Seattle, but nobody from Seattle goes there, so it often has reservations available when all the closer campgrounds are booked http://www.parks.wa.gov/parks/?selectedpark=osoyoos%20lake

Closer to Seattle, Lake Kachess is a fun spot not too far past Snoqualmie Pass. I had a lot of fun summer weekends up there as a teenager, and managed to stay out of the Kittitas County Jail. http://www.reserveamerica.com/campgroundDetails.do?subTabIndex=0&&contractCode=nrso&parkCode=kach

On the other side of Puget Sound, check out Kitsap Memorial State Park. This is a great park that I just discovered, they have yerts and cabins, and a nice waterfront on Hood Canal. It is also one of the few public places where you can harvest oysters with a WA fishing license in most years, although it is currently closed. http://www.parks.wa.gov/yurtsandcabins/kitsapmemorial/

On the coast, the "numbered beaches" in Olympic National Park are a lot of fun too. They are just identified as "beach 1, beach 2" etc. You can camp right on the beach, no reservations, just find a spot and plop a tent, but be prepared to hike a few miles in to camp, and no dogs allowed. I got kicked out of there last time for having a dog (I didn't know). http://wikitravel.org/en/Olympic_National_Park

Hope this is useful. Washington is a beautiful place, get out there and enjoy it! Sorry for my un-embedded links. The last several times I have tried embedding links on Qland it hasn't worked.

And remember if you do cross the mountains or take a ferry, pack your patience. Passes close, ferries run late, shit happens. Remember that half the fun is getting there!