About 3 hours west of Spokane you'll find some awesome hiking and scenery in the Washington Cascades. Below is a link to a trip to Waptus Lake I took with the wife a couple of years ago. I've spent time in the southern section of Alpine Lakes and in the Goat Rocks wildernesses and both are great areas to backpack in. There's great stuff farther north too but I haven't been there... yet...
Alpine Lakes Wilderness: http://www.fs.fed.us/air/technical/c...php?recordID=2
Goat Rocks Wilderness: http://www.fs.fed.us/air/technical/c...hp?recordID=29