You'll be passing through some amazing country, so it would be a shame not to stop and see some of it. You should plan a stop to see Yellowstone and Grand Teton. From there, the most logical route is to cross Idaho and then wind up in Ontario, Oregon on I-84, then take continue all the way to Portland, north on I-5 to Olympia, north on Hwy 101/3 to Bainbridge. It's correct that you don't want to come west on I-90 and wind up in Seattle.
How you cross Idaho might depend on your time frame. I-84 is the fastest from the Yellowstone area, but there are routes through the mountains, such as Arco-Stanley-Payette, that feature awesome scenery. Also, set aside a little time for the waterfall drive on Historic US 30 just east of Portland. You will also be passing near Mt. St. Helens with this route--worth a side trip.