there is a great drive from hwy `12 near Yakima to hwy 410 over mt. Rainier. You could take that going or coming. Its very spectacular and the nicest route I have found from E Washington over Mt. Rainier. Its very nice. On I-90 right before the summit is the town of Roslyn where they filmed northern exposure for over 6 yrs. Its kind of a fun spot and right off the freeway.
The rain forest would take a big chunk of time to get to and back. There is a lot of old growth forest areas near Rainer that are a good alternative.
Or if you come back over Hwy 2 Leavenworth is a neat stop. Baviarin themed village in the middle of the cascades
With only one day in Seattle, I would wander around Pike's Place Market, maybe take the underground tour. Then on your way to Spokane take Hiway 410 and stop in Mt. Rainer Nat'l Park (they have a good website). You could drive on to Yakima or Ellensburg, Hiway 821 between Yakima and Ellenburg is a nice drive, beautiful scenery, but look out for deer in the evening and early morning. From Ellenburg it's only about 2 1/2 hours to Spokane. In my opinion I'd miss Grand Coulee Dam. If you drive straight from Spokane to Seattle (takes about 4 1/2 hours) you could have a couple more days in Seattle or by driving a bit further go to Olympic Nat'l Park and the upper coast. There's a banana belt type microclimate in the Sequim area if it's raining elsewhere. Hope you have a great trip; I'll be out in the Boston area in Oct. myself!
Thanks for the ideas. If you need any info for the Bos trip, let me know.