Doctor Baker's Walla Walla & Columbia ran from Wallula to Walla Walla. Extensions to the east brought it to the foothills of the Blue Mountains. The initial OR&N and NP track at Wallula was built to 36 inch gauge to allow use of the WW&C equipment until the NP and OR&N actually connected to their track. Initially, the steamboats were the connection.
Several logging railroads operated in eastern Washington. Edwards & Bradford / Consolidated Lumber Co. ran four small Shays on their railroad out of Elk, north of Spokane. Consolidated's railroad closed by 1930. Biles - Coleman Lumber Co. had two narrow gauge operations, the longest and longest lasting running east from the mill at Omak, which lasted until after WW II. The B - C line was the subject of a book by John Lewis, _Reservation Narrow Gauge_, which is long out of print and commanding premium prices.
I'm aware of references to a narrow gauge mining tramway near Boyds, Washington, but haven't much other information about it.
Thbe usual contractors railroads of 24 and 36 inch gauge were used on some railroad construction and some public works projects in eastern Washington.
Cheers!
Charlie
CVM