Our family took our first cruise last summer and we had a blast! Even when we didn't have an excursion set up at each port, we still got off the ship and explored, shopped, went to a beach etc.
Our favorite excursion was a Land & Sea tour in St. Croix. It included an ATV tour in the mountains and then jet skis, kayaking and snorkeling at a beach. So much fun. A little pricey but totally worth it. We would have been satisfied having this single excursion for the entire trip!
This is a separate excursion that you book on your own, not through the cruise line. At first I was concerned about that, but with this company, if your ship does not arrive at port, you do not pay. Our ship had to change itineraries so we arrived on a different day than scheduled, and they still were able to honor our reservation. Make sure you don't book any excursion outside of the cruise unless they have that same policy. Many hold you accountable regardless if your ship arrives or not. And I guess it is common for ships to change their course throughout the week due to weather.
Also, check out www.cruisecritic.com for insider suggestions and recommendations. This site is very helpful with general cruise info as well as recommendations for excursions.
Have a great time!