Now I'll let you in on a secret. Sunny weekend afternoons regularly fill up the day use parking for the beach. What most people dont know is that there are two additional parking areas/beaches that dont get the use the main beach(West Beach) does. North Beach and the Ampitheater beach will still have alot of parking and tons of open beach space when the West Beach is wall to wall humans. Goto North Beach and walk west along the beach and you'll pretty much have all the space you want.
Enjoy

http://parks.wa.gov/parks/?selectedpark ... ion%20Pass