Well it's Spokane, so off your back porch
Sorry, originally from Seattle so I have to make fun.
I'm sure some people will chime in, but I've gone into the Cascades (public lands) with weapons and had no problems. Ask the people, once you get there, where they go...or if you're out driving around and see hundreds of shotgun shells and empty brass, there's a good bet you can shoot there no problem. Fire roads and logging roads are good starts, you're also right next to Idaho (Rocky Mountains) and there should be no problems finding somewhere in there.