Caribbean cruises from Charleston mainly go to the nearby Eastern Caribbean, but there is a longer cruise to the Southern Caribbean also. The cruises are on Carnival Cruise Line. See the schedule below.
Grand Turk is a stop on some of the cruises. It's a small island in the Turks & Caicos chain, located east of Cuba. The Grand Turk cruise center has beaches with palm trees, a big pool with cabanas, and good snorkeling. The Margaritaville bar and restaurant are popular, as is the FlowRider surfing simulator.
Amber Cove is a private cruise port in the Dominican Republic. Puerto Plata, founded by Christopher Columbus and the first European settlement in the Americas is close. You can explore Fort San Felipe and stroll the 3-mile Malecon boardwalk with restaurants and shops. Swim with dolphins at Ocean World.