On Barbados: The five-star catamaran champagne lunch and snorkel tour is pricey but worth every dollar. You get a lovely ride up the coast, snorkeling off a beautiful white sand beach, and a great lunch of local fare (flying fish, chicken, salads, bread, dessert and for those who want it --champagne!) The ride back is equally lovely with passengers just relaxing and reflecting on a perfect day -- a nice alternative to those "pirate rum punch rumbas"
Or--grab a cab at the shopping mall a short walk from the ship (fares are clearly posted) to one of the beaches. You can arrange with the cab driver to return to pick you up--the beaches are lovely and you can rent water sport equipment on most beaches or go for a parasail.
Bonus: You can buy tropical flowers for a reasonable fee in the shopping mall for your cabin--hibiscus and antherium in a a lovely bamboo vase.
On St. Lucia: If you are a land lover--take the jeep tour to the rain forest, but my favorite is taking a sailboat or cat up the coast toward the Pitons. The lush beauty of the island is spread out for your viewing pleasure. If you are feeling ambitious, you can take a short drive up the coast to a spot where you can rent kayaks. This tour is for folks who want to get quite q bit of exercise because after kayaking your way back down the coast (with flying fish sometimes landing in your kayak) you land on a rocky beach, then swim out to a boat and then go on to snorkel!
Can't help with Antigua--maybe another poster can?