Indy is right about the Northern Tier - but -
It can be a bear of a start for a relatively inexperienced tourer.
By the third day you are doing big climbs - up to Rainy Pass -
And, to add insult to injury, a steep drop and then up Washington Pass.
Plus there are four more passes before you reach Idaho.
It's a beautiful route, but lotza climbing right out of the gate.
I done all the legal crossings of the Cascades in Washington -
(Plus one that was - maybe - illegal. Hiked/Portaged my bike, didn't ride.)
I have a posting over at Crazyguy on the Washington passes.https://www.crazyguyonabike.com/doc/?o=tS&doc_id=13664&v=1M
Chinook Pass on Hwy 410 is, by far, the most beautiful and has the least traffic.
From the summit at Tipsoo Lake you have wildflowers and a stunning view of Mt. Rainier.
The pass doesn't open until Memorial Day and is snowed in until July 4th.
(I did did June with snowbanks and fog.) But in early August it is heavenly.
There are two ways to hit Chinook Pass from the west -
1) Using Hwy 410 thru Enumclaw or 2) US 12 / Hwy 123 thru Morton
East of the pass are the magnificent American and Naches valleys with riverside camping.
As for the other passes:
Stevens Pass / US 2 - Moderately heavy traffic with little to no shoulders at times; worst choice.
Snoqualmie Pass - Can use I-90 (Why?) or unpaved John Wayne Trail and old service roads; tricky but doable.
White Pass / US 12 - Moderately low traffic, good shoulders, nice east side - but why not Chinook if you are this close?
Columbia Gorge / Hwy 14 - Moderately busy, shoulders variable, some remote stretches.
Not sure if you want to start on the actual Pacific Ocean or just on salt water. (Different strokes)
As I said earlier, the San Juan Islands are really sweet as a starting point.
You can take a pricey catamaran ferry from Seattle and back.
Or you can take an airport shuttle straight to the Wash. State Ferry docks in Anacortes.
Or you can take a shuttle out to Aberdeen and start at the Westport Lighthouse.
There are a number of routes from the coast to Chinook or White Pass.
ACA has a good portion as part of their "Washington Parks" loop - https://www.adventurecycling.org/routes-and-maps/adventure-cycling-route-network/washington-parks/
But a route with less traffic and climbing is via Raymond, Chehalis, and Morton.
If interested - send me a private message and I'll offer you any specifics I know.
Best - J
PS - The Prism climate site at Oregon State Uni. has excellent temp/precip maps of the U.S. by month.http://www.prism.oregonstate.edu/normals/