Once crossing into WA, I would suggest US 2 west from Spokane and go to Grand Coulee Dam and watch the laser show on the face of the dam.
I would suggest crossing the Cascades either on US2 or WA 20. US 2 passes through Leavenworth which has a Bavarian motif. WA 20 goes through the north Cascades Natl Park, along the way is Winthrop which has a western motif.
Any plans for Glacier Natl Park/
Not sure what time frame you are planning on trip. Rockies and the Cascades can have shifts in the weather in mid to late Sept.