Is it better to take a shore excursion or explore ports of call on my own?

A lot of that is really up to you. Most ships include a program of their shore excursions with your cruise documents, but, if not, you will have one in your cabin when you board the ship. Lots of the sailing and snorkeling excursions are tons of fun and much easier than trying to arrange them yourself. Some of the islands/ports that are easy to explore on your own (by cab, or even on foot in some places) are: St. Thomas, Grand Cayman, Key West, Freeport, Cozumel, San Juan and Bermuda. If you’re not the real adventurous type, consider a shore excursion in at least one port.