Hey! Welcome to the site. I love rabbit hunting, but I have to admit that I don't have a single good western washington public land spot. And if I did, I wouldn't share it on the internet!
A lead for you though:
A few years ago I saw a ton of rabbit tracks in and around the thick brush in the first mile or so of the trail going to the Greenwater Lakes (up FS70, near Enumclaw). I was there in December with fresh snow on the ground. I always wanted to go back and poke around the brush with my shotgun, but I never got around to it. I've since moved to Oregon and doubt that I'll get up there. Strap on some snowshoes and check it out for me, please.
But if you actually want to be successful, get permission on private land. The best rabbit hunting on the westside is in pasture on small farms. Get permission, show up before dawn, and walk the edge of the blackberry hedges. They'll be two hops from the thickets where you can spot them and shoot them in the head with a 22.