Brainbridge Island is a fun, quick getaway from downtown Seattle, and access via public transit could not be easier. Just walk down to the Seattle waterfront, follow the shore to the Colman Ferry Dock, then hop on the boat to Winslow for a scenic half hour cruise across the Puget Sound. There is not a lot of hiking near Winslow but the town is worth a few hours of time. A short trail connects the ferry dock to downtown Winslow - look for the start of the trail beyond the tollbooths at the entrance of the ferry loading lanes, on a driveway leading to a waterfront condo complex. The trail crosses a slough, then ends in a waterfront park. Downtown Winslow with its shops and cafes is located nearby on Winslow Avenue. Find a coffee shop, sip a latte, and relax.
If the tide is low, you can walk through the condo complex to the waterfront, where you can access on the beach. From there, you can walk underneath the ferry dock and onward along the beach for a considerable distance.