Maybe way more than you want - but here goes.
Here are traffic count maps for:
Possible initial segments:
US 30 - South side of Columbia - 77 mi; +3680 elevationhttps://ridewithgps.com/routes/18958632
WA 4 - North side of Columbia - 80 mi; +3750 elevationhttps://ridewithgps.com/routes/18960513
WA 8 - Willapa Hills - 78 mi; +2820 elevationhttps://ridewithgps.com/routes/10737575
US 12 - Chehalis Valley backroads - 76 mi; +1000 elevationhttps://ridewithgps.com/routes/10724974
Look at the elevation profiles - way different. The Columbia River routes have lots of ups and downs. The Willapa route has a single gradual climb. The Chehalis route is level.
Western Washington / Oregon
US 30 traffic volume is often 10,000 vehicles per day and 20,000 as you get close to Portland. For me that is insane. Yes, there is a wide shoulder and it is “technically” safe, but it sure isn’t pleasant. Plus a couple of moderate climbs.
The Historic Columbia Highway east of Portland is lovely and is used by many Portland cyclists, but it is narrow, with many steep ups and downs, and has a good deal of tourist car traffic.
WA 4 west of Cathlamet is lovely with low traffic and near-perfect vistas of farms and rivers. The camping park at Skamokawa has the most stunning view of the Lower Columbia. There are some good climbs. Traffic picks up east of Cathlamet, but the views remain great.
WA 14 has heavy traffic in the Vancouver metro area and a good deal all the way through the Columbia Gorge. And it isn’t flat. East of Maryhill it gets pretty remote, arid, and breezy. I rode this on my first X-USA trip back in 1987. Lots more traffic now.
WA 8 has low traffic and a parallel bike trail from Pe Ell to Chehalis. There is a gradual climb to the summit of the Willapa Hills. Rainbow Falls Park has great camping.
US 12 west of I-5 is a busy 4-lane highway, but there are quiet, parallel back roads all the way. The is the easiest route from the coast with almost no elevation gain. Moderate scenery.
US 12 east of I-5 is a great route through the Cascades. The main highway has only moderate traffic and good shoulders, but there are excellent back road sections with almost no traffic. There are a couple of views of Mount St. Helens and Mount Adams and lots of views of snow-capped Mount Rainier.
Even though White Pass on US 12 is at 4500 ft., there is more overall climbing on the L&C route through the Columbia Gorge.
Eastern Washington / Oregon
WA 14 is O.K. Light traffic and you should have tailwinds, but pretty barren with the views behind you. You cross back into Oregon and hit US 730 with moderate traffic and some nice river views. US 12 from the river to Walla Walla is pretty busy, but with safe shoulders.
US 12 on the east side is one of the finest rides in Washington state. Big vistas, canyons, and the rushing Tieton River. Back roads thru the Naches Valley orchards - cherry season in June. Two options to the Tri-Cities - the Old Inland Empire Highway thru the Yakima Valley or WA 24 / WA 240 which is more direct, but pretty empty. Pasco-Kahlotus Road is an empty, paved, road through dry country. What the L&C route misses is the most spectacular scenery in southeast Washington - Palouse Falls - which should be huge in June. A fantabulous overnight.
If you have a vehicle at Portland airport, I might suggest starting in Westport, Washington or at the Tokeland Hotel.http://www.tokelandhotel.com/home.html
A suggested route across Washington:https://ridewithgps.com/routes/18965206
Photo - Willapa Bay