You can place an ad in the classifieds or search the classifieds for listings by owners or agents. Another option is using real estate brokers or consultants to find you a place to fit your preference. The directory has listing of these agents and there is an association (Realtors Association of Jamaica) you can check with for licensed agent. The Real Estate Board licenses real estate agents.
Demand is high around business centres as New Kingston in St Andrew. The area known as the Golden Triangle, bounded by Hope Road, Old Hope Road and Trafalgar Road, brings together prestigious neighbourhoods in walking distance from an office for the person with active outdoors lifestyle. The apartments may have property managers that you can go through to assist with short term accommodation.
Demand for accommodation is also high around two universities located in Papine, eastern St Andrew. That area includes Elleston Flats, Liguanea, Mona Commons and Hope Pastures. The demand is driven by the need for off campus accommodation. Getting a flat is hard in these areas, especially for new students; and returning students try to settle accommodation arrangements one school year ahead before they break for the summer. Flat sharing is more common among students than by workers.
Nearby places to Papine such as August Town, Tavern, and Kintyre are cheaper options for accommodation due to the lower perceived prestige of the neighbourhood.