How much of the Caribbean do you want to see?
Rough, crude guesses -- maybe someone with real experience in a not-too-big not-too-fancy boat can check these:
Auxiliary sailboat -- less than one gallon per hour, fuel-only cost less than one dollar per mile when powering. Sail and rigging repairs
and replacement cost maybe something like twenty-five to fifty cents per mile for economy sailors on an older, say 32- to 35-foot boat???
or semi-displacement trawler
cruiser -- one to four gallons per hour, fuel cost maybe a dollar up to a few dollars per mile
Semi-displacement old-fashioned motor
cruiser (not particularly fast, maybe about 35'), ten to twenty gallons per hour, maybe three dollars per mile?
cruiser or cabin
speedboat -- fifteen to one hundred gallons per hour; one mile per gallon or four dollars per mile in the 30-foot range, up to ten to twenty dollars a mile for the bigger, 40' or so boats. If you have to ask about fuel cost for long-distance fast motor yacht cruising, then you can't afford it.
Note also that the smaller cruisers (30-foot range) may only have enough fuel for a range of about 250 miles or less at speed, less for rougher weather
and more range if moving slowly (but probably uncomfortably; mpg's might double or triple at trolling speed of 5 mph or less). This affects which voyages you can make and your ability to turn around if conditions deteriorate mid-passage.