You have a number or considerations:
1. Where to cross the Columbia River
2. Where to cross the Cascades
Not as easy as it seems.
There are great crossings over the Columbia at Wenatchee,
but US 2 on the west side of the Cascades sux - narrow, dangerous, heavy traffic.
The Iron Horse Trail from Ellensburg to just east of Seattle is great,
but the crossing over the Columbia is I-90 with no shoulder.
Hwy 20 over the North Cascades is stunning.
You can cut up to it from Plummer, Idaho
via Spokane, Wilbur, Grand Coulee & Twisp
Then cut south after crossing the Cascades via Arlington.
You would be best to access Seattle via the Burke Gilman Trail.