I live just outside Seattle. Let me know your schedule and we could arrange a meeting. As for 'must sees', there are very few things to see at all in the line of American period furniture. The Seattle Art Museum has about six pieces on display. But if you expand your interest in historical woodworking to airplanes, there is Boeing's Red Barn at the Museum of Flight. There is also the Center for Wooden Boats on Lake Union.
As I think I have mentioned before, I am manning an existential outpost here.
Peter Storey Pentz