Yellowstone to Seattle

Go to Bozeman then hit I90 west. Takes about a day and a half.

From Yellowstone exit at west entrance to city of West Yellow stone. Take 191 to Bozeman Mt. In Bozeman get on I-90 it takes you right to the state of Washington.
The trip through Gallatin National Forest to Bozeman is beautiful good rode all the way, main route to Bozeman. Many things to see in Bozeman big Dinosaur museum at the collage. Jump on I-90 to Washington enter at Spokane. In Butte there is a real nice mining museum. Nice drive all the way. You can go on into Idaho Falls get on I-15 and end up at Butte but adds a good 90 miles to the trip. Or, drive through Idaho on I-84 to Oregon then cross over. It's 800 miles to Portland from Idaho Falls. I've been both ways. Big wide roads through Idaho, very nice roads though Montana, and most likely shorter looks like the boonies but is not.
Been to Seattle one time, did not want to go back. There are so many hills in that town they name them as neighbor hoods. I bet there are a lot of brake shops in that town. Nothing against Seattle, the place did not appeal to me.

Since you mentioned, "baked potatoes," why not check out the Idaho Potato Museum....:)

LINK

Another option is to head west on US 20. Along the way, you can take in Upper and Lower Mesa Falls and later Craters of the Moon National Monument. If's you fish, the Henry's Fork of the Snake river will ring your bell. This route drops you down to the Interstate which would take you south of Seattle via Portland. Another option is to take US 12 out of Missoula over the LoLo Pass, another good road off the Interstate Highway system.

Glacier NP is beautiful, and US 2 passes directly through on the way to Redmond, just north of Seattle. Although US 2 is a 2 lane highway most of that way, it is a beautiful and gentle road. I've been across there towing a 21 foot TT, and would take that route again any day. Not quite the most direct route to take, but worth the extra miles, IMHO.