It has been a long time since we were there ('97). We found places to overnight in a few state parks as we drove up the coast (never with hookups), never with reservations. We did a week end at a state park just north of Newport...next to the beach if I remember correctly.
This Seems Like The OneIn '86, we enjoyed several days just above Astoria at Cape Disappointment State Park (formerly Fort Canby State Park), a 1,882-acre camping park on the Long Beach Peninsula, fronted by the Pacific Ocean. It was a very large place, some camping near the beach (full it seemed) but a lot in an open glasses area. But it has been a while.
It might have some first come, first served sites, worth a call.
http://www.parks.wa.gov/parks/?selectedpark=Cape%20DisappointmentThe park offers 27 miles of ocean beach, two lighthouses, an interpretive center and hiking trails.
Visitors enjoy beachcombing and exploring the area's rich natural and cultural history. The nearby coastal towns of Ilwaco and Long Beach feature special events and festivals spring through fall.
The campground was Walking distance to Cape Disappointment Lighthouse which began operating in 1856, and is now the oldest lighthouse still in use on the West Coast.
Weekends are notorious for being hard to get into in most places. Good Luck.