If you have the time, stay off the Interstates when you can. I drive often between the Tri-Cities and Eugene, if was going to scenery and not rushing it I'd take Hwy 14 (WA side of the Columbia River) to Hwy 97 South (don't go further on Hwy 14), take Hwy 97 south, you'll get some amazing views of the Cascade Mountains. From there you can cut across to I-5 by taking Hwy 126 all the way or cutting of at Hwy 20.
From Spokane you can go down to Hwy 395 but it might as well be an Interstate. I think I'd go south on 195 and head to Palouse Falls SP then down 260. You'll see a lot of the scaring done by the Ice Age floods through there.