Panama City is warmer and not in the hurricane zone. While very Americanized due to the former U.S.-owned Panama Canal Zone -- to say nothing of the large ex-pat community that lives there now -- it has a lot of Spanish colonial heritage. Plus, it's very affordable. Like ridiculously cheap, especially Uber. Business-class out of FLL/MIA/PBI via ATL is pretty consistently +/- $1200 through the end of the year. Economy is as low as $470-ish. Upgrades are pretty easy on this route.

Business-class to Bogotá is under $800 for much of September, October and November, according to Google Flights.

Another affordable option is Santo Domingo, the capital of the Dominican Republic. Google Flights shows business-class through spring 2018 between $700 and $900 on most dates from your preferred airports.

If you're adventurous, what about Haiti? There's a wonderful new Marriott there. There are lots of $600-$800 business-class airfares from MIA to PAP, aka Port-au-Prince.

Havana looks to be under $600 almost every day, including peak spring break next March. Heck, you could book economy (+/- $205) and just go there for dinner!

If you're up for a mileage/status run, FLL to SIN (Singapore) is consistently pricing at $792 in economy-class through next spring, based on a quick Google Flights search. Here's a sample trip: https://goo.gl/flights/4gU1. You could use Singapore as a base to explore other countries and destinations in Southeast Asia and the Pacific.