A half an hour drive down the Norman Manley Highway from Kingston, bordered on both sides often quite narrowly by the harbor on one side and the ocean on the other, is the small town of Port Royal. A sleepy town that has seen devastation from numerous earthquakes, it is a far cry from what used to be the richest and "wickedest" city in the world and a long ago safe haven for the most criminal pirates on the sea. There are still remnants of this taboo glory, but its mostly in the ruins of what has been left behind.
Popular attractions include Giddy House, an old artillery storehouse known for being extremely canted and an interesting photo opportunity. Otherwise, your most interesting prospect is Fort Charles, the oldest surviving structure in town. Built by the British in the 17th century, it is notable for its ancient brickwork, and its museum, which displays artifacts that have been recovered from the large parts of Port Royal that have been submerged by natural disasters.
Note:It is interesting to note that Port Royal is known in the archeological community as the most important post-medieval site in the Western hemisphere, all the more interesting because there is still much of the city buried beneath the ocean waves.