I know of no public land that has them. There used to be some private ground between Moxee and Prosser that we shot squeaks on several years ago. Personally, my wife and I didn't really like it, as there were too many houses, that were too close to be able to sit in one spot and shoot. All we brought were rimfires, and it was too tight for that. The property owner used a pump pellet gun.
We just drive the extra couple hours, and go South. The weather is usually better there anyway.