Fay-Bainbridge State Park (206/842-3931, www.parks.wa.gov [1]) covers a mere 17 acres but it offers some of the finest over-the-water vistas of the Cascades and the twinkling lights of Seattle [2]. It is a delightful place to escape the city. Fay-Bainbridge also offers campsites in the trees ($19 for tents; $27 for RVs), plus hot showers and beach access with scuba diving and boating facilities at the island’s northeast end.
This is the closest public campground to Seattle—just a ferry ride and short drive or bus ride away—so it is very popular in the summer months. The park’s open for day use year-round but only open to camping mid-April to mid-October.
Links:
[1] http://www.parks.wa.gov
[2] http://www.moon.com/destinations/washington/seattle