Lived on whidbey most of my life...theres some public land to hunt. I usually hunt private, but I believe the Kettles Trail system and Trillium Woods are public access hu ting. Would need to confirm with wdfw to be sure if they're still open. I agree with Special T, bow will be the most likely to get you on property here as people dont like some of the problems that come with guns etc., but I mainly hunt muzzy and have very good luck towards the end of October.
Dress nice, wash your rig, and use your manners and after asking around a bit you will find some property. I've found several properties to hunt in the last few years here, 9 out of 10 is a no, but you dont know til you ask. Send me a PM if you want. Theres a ton of deer here