The Leavenworth idea ain't bad... but east of there is pretty bland. However, some of the best hiking in the state is in that area, up Icicle Creek.
Further north, Highway 20 is just open in the last week or so- that would be my suggestion.... north to Mukilteo, ferry to Whidbey, through Deception Pass, over to Mt. Vernon (much cooler little downtown than Burlington, if you're looking for a place to get lunch). Back up to 20 and along the southern edge of the NCNP.
Three options from there:
When you get to Twisp, you could go south on 153 to Chelan (Lake Chelan is nice) and then head east to Spokane... high desert vistas
Follow 20 to Omak, then 153 through Grand Coulee (DAMN!) and then onto Spokane
Follow 20 all the way to Colville, then 395 into Spokane (more green/mountains)
If I was with my father in law, we'd do the dam (he's a bridge engineer). If it was just me, I'd take 20 all the way to Colville, and then into Spokane (I'd probably car-camp and do some day hikes). If you're looking for some hiking options, here's your best resource for trails and such: WTA Database
So, I guess it depends on what your hopes are for siteseeing and what your plans are for lodging.