Eastern WA and OR are beautiful in a different kind of way, but it is a lot of nothingness, heat, and dry grassland. I agree it might be nicer to head directly West from Spokane.

Northeastern WA is very beautiful. I'd recommend heading Northwest to Curlew and then Winthrop. From there maybe take a ferry over to Port Townsend. You could also head up to Canada and then head West.