Although that may look like a direct way to get to Cartagena -
Florida ->
Jamaica -> Cartagena - - please look at the Atlantic Pilot
Charts and you find it is a rather nasty way to get there. There are two "reasonable" weather-wise routes;
Bahamas to T&C to D.R. - Samana then south to the ABC's and west along the coast to Cartagena ( a rather long
route but out of the nasty circle of
water between Jamaica and
Columbia. Another route is from Jamaica to
Panama via Providencia, St Andres and
Panama then east to Cartagena. This is shorter and also avoids the nasty area between Jamaica and
Columbia - but May is not a good month and as the season gets on the early Tropical Storms start up first in the western
Caribbean in June.
There is only one marina in Port Antonio and they have a website and advertise in all the sailing/cruising publications. The rest of Jamaica is not particularly safe for visiting boats so be wary and careful.
However, if you have a "green-water"
boat and experience with gales and monster seas, then the route from Jamaica to Cartagena is do-able.