Consider Anacortes or perhaps even La Conner. It puts all of Whidbey Island within reach (Rosario Beach, Deception Pass, Fort Ebey State Park, Ebey's Landing) but you could also do day trip drives up Chuckanut to Fairhaven and Bellingham. Good hiking in and around Larrabee State Park and Samish: Oyster Dome, Lizard and Lily Lakes, Fragrance Lake, Pine and Cedar Lake. I believe there is a fair amount of mountain biking around Blanchard Mountain, too.

Folks have already mentioned the pillow basalts on display in the Olympics, but it should also be pointed out that the eastern Olympics seen from Seattle are part of the Crescent formation which is made up of oceanic basalt. Look into the Siletzia story. There was a Hawaii or Iceland-like island that formed off the coast of Oregon millions of years ago and eventually accreted onto the western coast of North America. This means the northeastern and eastern Olympics are geologically quite distinct from the interior and western Olympics. In my mind you can kind of sense it when you peer into the range from atop peaks like Mount Ellinor and Mount Townsend, or even standing on Hurricane Ridge.