There are many all-inclusive resorts in the Caribbean, at many different price points. Most travel agents can set you up with a program that includes transportation between the airport and the resort, either via tour bus or something private, whichever you prefer. Jamaica, Punta Cana (Dominican Republic), St. Thomas, even Cancun/Mexican Riviera - which is considered part of the Caribbean - are just a few of the most popular.
Lynn-Critter Lover!
(especially cats!)