The Puget Sound Navy Museum sits directly opposite the Bremerton ferry terminal in a former Navy Yard fire station and tells the story of the Pacific fleet and the shipyard that supports it. Exhibits cover everything from the launching of the Maine in 1895 to recent carrier overhauls; standout pieces include a working bridge simulator, large-scale models of every carrier ever based on the West Coast, and salvaged hardware from a century of work in the dry docks.
Admission is free, and the museum is small enough to do thoroughly in an hour. Combine it with the USS Turner Joy next door and the short waterfront walk through Harborside Fountain Park for a complete waterfront half-day, all within five minutes of the ferry.