Princess offers one of the most comprehensive scuba and snorkel programs around, with PADI-certified instructors aboard all vessels on Caribbean itineraries and a comprehensive array of shore excursions from introductory to advanced. If you are a beginner and are not familiar with the area, it's probably best to take one of the organized excursions from the ship -- which also have the advantage that, should a group be delayed, the ship will await its return before leaving the port.
If you are a seasoned snorkeler and you really do feel comfortable going off on your own, you certainly can do so. If you are not familiar with the area, do obtain information from either the instructors on the ship or a local operator as to where the best spots are for your particular interest.
You might want to check out some of the standard shore excursions, too, as some of them offer unique snorkeling opportunities. From St. Thomas, for example, the ship offers a "Champagne Catamaran Sailaway to St. John" for swimming at a pristine beach and snorkeling around a nearby reef. The crew of the catamaran even provide snorkeling instructions for beginners and a pre-snorkel brief. Likewise, on Grand Cayman, there's a shore excursion to swim with the (semi-tame) stingrays at Stingray City.
Have a great cruise!