Pierce's Summer Resort was on the Duckabush River, on the Hood Canal north of Lilliwaup and just south of Brinnon.
This image is courtesy of Dan Kerlee.
There is also an Image 280 (280 - Compliments of Hoo-Hoo House A.Y.P.E.) from the Alaska Yukon Pacific Exposition. Perhaps Otto reused the image number because no one would be interested in an A.Y.P.E. card after the exposition ended.