The space in the Castle of St Peter that was once used to store booty collected during underwater archaeology missions, now houses Bodrum's Museum of Underwater Archaeology. It is arguably the most important museum of its type in the world, a veritable lesson in how to bring ancient exhibits to life. Items are creatively displayed and well lit, and information panels, maps, models, drawings, murals, dioramas and videos all help to animate them.
It's undoubtedly one of the best museums in Turkey, not to mention the Mediterranean (and could teach some of the cupboard-like Victorian museums in the West a thing or two!).
The views from the battalions are spectacular and worth coming for alone. As the museum is spread throughout the castle, you'll need at least two hours to do it justice. Arrows suggest routes around it (red for long; green for short), but guides are not available. There are plans to open a Mycenaean room in the future, and to install a lift.