There are no major cities in the "Rocky Mountains of Washington" because the Rocky Mountains do not extend into Washington State. The Rockies' northern terminus is generally considered the Liard River in northern British Columbia, Canada—roughly 600 km (370 mi) north of the Washington border.
Washington is defined by the Cascade Range (volcanic peaks like Rainier, Baker, Adams, St. Helens) and the Olympic Mountains (a distinct, non-volcanic range on the Olympic Peninsula). Major cities near these ranges include:
If you're seeking "Rocky Mountain" scenery in the U.S. Pacific Northwest, look to northeastern Washington's Selkirk and Kootenay Mountains—geologically part of the Columbia Mountains, not the Rockies proper—or cross into Idaho and Montana where the true Rockies begin.