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The Pacific Northwest is mostly public land once you get out of the valley. The Cascades and the coast range are great places to hike, and the more arid areas on the east are cool for camping and elk hunting.
I'm a forester in Oregon so I'm out in that land a lot. As long as you don't have a firearm you're allowed to be on gated government land when it's not hunting season, and there are huge amounts of unused forest in the cascades and the northwest corner, as well as good trails. The Gorge in the north is really great to be out in as well if you're okay with cold nights.