“Floribbean” is “Florida” + “Caribbean.” National Airlines advertised “Floribbean” vacations in the 1960s. In the early 1990s, “Floribbean” became the name of the Florida-Caribbean cuisine that uses native plants and local seafood.
 
 
12 April 1961, New York Times, pg. 32 ad:
MIAMI BEACH—NASSAU, BAHAMAS
We call it “The Floribbean”—you’ll call it the greatest vacation idea ever!
(...)
National Airlines
 
29 April 1962, Los Angeles Times, pg. K11:
National Airlines begins its 14th consecutive year of spring and summer vacations with a program which will highlight both Florida and the Caribbean.
(...)
These Floribbean vacations combine the glitter of Florida’s Gold Coast with the charms of the Caribbean. There are island-hopping cruises to all of the major Caribbean Islands.
 
10 May 1992, New York Times, “Florida’s Chefs Add Exotic Fish to Menu” by Cynthia Hacinli, section XX, pg. 6:
It all began with something called Florida cuisine, a fusion of southern, Cuban and Caribbean influences (this last has led some to dub the resulting hybrid Floribbean). The new approach calls for the use of local or regional fruits, vegetables and herbs—and, of course, fish.
 
17 June 1992, New York Times, “Hear About the Restaurant That Went to Miami and Stayed?” by Florence Fabricant, pg. C3:
As for the food at the new restaurants, aside from the fare at Victor’s Cafe, the menus make no attempt to rattle New York or European appetites with new wave “Floribbean” cuisine, a fusion of Caribbean and New American cooking based on tropical ingredients.