Can't recommend for all, but can for a few.
Montego Bay is a place where I personally would stick with a ships tour. Whatever it is you do I just feel that Jamaica is not a place to go wandering on your own. There are many options including a long trip to Dunn's River Falls , rafting on the Martha Brae, visits to the "Great Houses" as well as well as golf and beach options.
Puerto Limon, look into the Torteguero Canal tour. Great way to see the countryside and great tour. We saw birds, flamingos , vultures , monkeys, sloths, crocadiles , banana plantations , and much much more.
Cartegena- This is one of the great beautiful cities of the old Americas. The history here is 500 years old. The city is divided into 3 areas 1) the historic old city, 2) the new city (looks like Miami), and 3) slums and the worst concentration of squaller and abject poverty you may ever witness. This is definately a city to see , and most definately one not to be done on your own. Take a comprehensive tour that takes you to the Cathedrals, the Monestary, the forts, the Old City and the shopping areas. Do not even think about striking out on your own, but do go to see what you can.