I think you're right about the Quinalt River Inn! Beautiful area. I always pictured the hotel as being a more anonymous chain place - this one looks rather peaceful. I bet when they remodeled the rooms they took out those lower-hanging clothes racks.
It was so poignant to see his blue plaid shirt on the chair - I immediately recognized it and felt so sad. Something unusual I noticed in the photos (from astridxx's international (!!) link) was the towel beneath the belt around his neck. Hotels usually have white towels. Perhaps he brought it with him? Was he seen with a backpack initially but it was never found? I will have to go back and read.
I'd never thought about it before, but some of the websites about suicide by hanging mention putting a towel or padding on the front quarter of the neck to keep the ligature from cutting into the skin.
There's a good synopsis and those same photos on this blog:
http://uidmysteries.blogspot.com/2014/05/the-mysterious-case-of-lyle-stevik.html