The state parks are awesome. Your first stop should be Cape Blanco State Park. They don't accept reservations but if you get there early in the day you'll get a site. Beautiful large sites, a lighthouse to tour and a practically secluded gorgeous beach. It's near Port Orford on the south coast.
We've also stayed at these state parks: Bullard's Beach at Bandon, Carl Washburne at Florence, Beverly Beach at Newport, Harris Beach at Brookings and Fort Stevens at Astoria.