While I'm sure a lot of folks here are anti-cruise, we had an amazing time on the SeaDream out of San Juan last early April. I'm definitely anti-big cruise myself. They claim to be a "yacht club" rather than a cruise and max out at 112 passengers. Able to dock at a lot of the smaller ports, and serve some of the best food I've ever had. 96 crew members from all over the world.
We hit Culebrita (nature preserve island off Puerto Rico), St. Thomas, Saba (very cool volcanic island), St Barts, Anguilla, Tortola, Norman Island, and Jost van Dyke on a 7 day trip. You can explore the islands on your own, or they organize 2-3 different activity options per port. Enjoyed it more than any other Caribbean resort experience.
https://seadream.com/voyages/search/destinations/caribbean