Book shore excursions if they are in your budget. Do different things at each port. We just did a 9 day southern caribbean cruise and we rode down the waterfalls in the Dominican Republic, did a beach day in US Virgin Islands, did a history tour in Antigua, etc. We used to get off at the ports and do stuff on our own and I felt it was less impactful than with a guide to tell you the history and details.

Have fun on the boat, they have tons of activities and you can experience new foods, have decent entertainment acts and funny games. Some are outrageous but usually they are entertaining.

Don't get the internet package. If you can, stay off the web, the best part is disconnecting from the world and just have fun.

Be disciplined - Cruise boats will try and have you buy as much stuff extra as possible. Set your budget before you step onboard and do not deviate. That cool artwork and watch that looks so fabulous on the boat all of a sudden loses the appeal when you get home and wonder if you really needed it.