@egardner is correct, NPA is the closest to you. Very close in fact! Here is their website http://nwpaleo.org/. @paul-kester is a member there. They have a lot of nice people and work closely with the Burke Museum at the University of Washington. Many of their members also belong to Friends of Stonerose up in Republic, WA (http://stonerosefossil.org/) and the North America Research Group (www.nargpaleo.org) in Hillsboro, OR. If you want to collect in WA, I would highly recommend joining NPA since it has become harder for amateurs to collect and they do partner digs with the Burke. @paul-kester is a great resource for collecting laws and regulations in WA.
What sort of fossils are you interested in?