How much work are you willing to do?
The Vantage Highway from Vantage to Ellensburg has light traffic.
But you have to do it early in the morning to avoid brutal headwinds.
(All the wind turbines on the ridgeines serve as important clues.)
Plus you avoid Hwy 24 and the Vernita Bridge.
A number of ways to do it:
1. Suck it up and ride the dangerous I-90 bridge. (Bad idea)
But it is doable westbound because of a significant downgrade.
There is a shoulder on the west side once you hit the causeway.
2. Make a reservation at the motel/campground in Vantage -
Then request a shuttle - they've been known to do this.
Of course, that means having a fixed date late in the trip.
* If there are concerts at the Gorge Ampitheater - the whole area is packed.
Right now there are multi-day events scheduled for mid and late Juy.
3. Radical. Take the spectacular Old Vantage Hwy down Frenchman Coulee.
Then chill out at the boat ramp at the river and hitchhike across.
** I've done this many times over the past 30 years.
Granted I was solo - also, it takes a chunk of time and is not guaranteed.
Or you could see if you could hire a boat shuttle.
Frenchman Coulee is worth it.
4. Cross on the Beverly Bridge then take Wanapum Rd north to Vantage.
Except that the completion date is Sept. 2021 - and will likely be later.
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The Palouse is magical - especially in late spring when it is green - -
https://www.crazyguyonabike.com/doc/page/pic/?o=1mr&pic_id=2666949&size=largeIt will be brown in late summer - still very nice with quiet back roads.
Pic - Frenchman Coulee