In addition to the campgrounds at Fort Ebey [1] and Fort Casey State Parks [2], you could try Rhododendron Park a Department of Natural Resources–managed park two miles east of Coupeville [3] on Highway 20. It’s easy to miss; look for the small blue camping sign on the highway.
Here you’ll find eight free in-the-woods campsites (with water) in a second-growth stand of Douglas fir trees, with an understory that includes blooming rhododendrons each April and May.
Links:
[1] http://www.moon.com/destinations/washington/north-puget-sound/whidbey-island/coupeville/sights/fort-ebey-state-park
[2] http://www.moon.com/destinations/washington/north-puget-sound/whidbey-island/coupeville/sights/fort-casey-state-park
[3] http://www.moon.com/destinations/washington/north-puget-sound/whidbey-island/coupeville