If you're staying in Kingston, set aside a couple of hours to see nearby Spanish Town. The town is well past its glory days—it was Jamaica's capital from 1534 to 1872, and the historic core is in near-derelict condition.
See the Georgian buildings, especially around the town square. The Cathedral Church of St. James, a beautiful example of Anglican architecture, is one of the oldest in the English-speaking West Indies (it dates to 1714). The small Jamaican People's Museum of Craft and Technology includes a re-created slave village.
15 mi/24 km west of Kingston.