I like to ride in the Colockum area. Its the mountains north of Ellensburg/Kittitas. Miles upon miles of logging roads which are open to non-street legal ORV's. You must have a license plate and tabs on your bike OR off-road vehicle tabs (either or will work, you don't need both). You don't need endorsements to ride there. You must stay on the green dot roads (white stick looking things with a green dot on the side of the road). Oh, you'll also need a Discovery Pass for your bike and your haul vehicle if you park your haul vehicle on State land.
Its really a neat place. Wide open sagebrush country to the east towards the Columbia River, and thick woodlands to the west towards Blewett Pass.
Some of the landmarks up in the area are Lion's Rock, Haney Meadow, Ken Wilcox Horse Camp, Wenatchee Mountain, Four Corners, Arthur Coffin Game Reserve, and Naneum Ridge State Forest.
Theres still is snow up high, but with miles of roads, you can still have fun sticking to the lower elevations for now.
Let me know if you would like any more info. I have lots of pictures and some maps of the area. I ride up there quite a bit, but I haven't made it up there yet this year.
I'm sure there are some places closer to you, but I haven't ridden in Western Washington very much, which is weird because I'm from Kent. Seems like most people make the trek over the pass to ride in Eastern Washington.