In Washington, if you continue on north, you can go through Deception Pass, then catch the North Cascades highway east across Washington. Both have some of the most spectacular scenery to be had as far as road trips are concerned. For some recent pics of the drive across the North Cascades my wife and I took, check out the first link in my signature.
Following that road all the way across Washington, just past Colville, you could take a detour (4x4 not needed) up to Radar Dome where you will find an old abandoned radar station.
There is also tourist trap town named Winthrop, made up to look like the old west that is kind of fun to stop in.
If you are traveling across Washington State, this would be my favorite route having the least amount of grasslands and desert. Though there are several ways and many other things to see, if you feel like going a hundred miles or so out of your way, or depending on which route you choose to travel. Since my wife and I live in the Seattle area, but we both grew up and still have family in the Spokane and Colville area, we are quite familiar with making trips across Washington.
Let me know if you have any questions about the area and I'd be glad to answer.