Did this cruise about one year ago, also on the Destiny. The itinerary has changed a little since then (I believe they added St. Lucia and dropped St. Martin, probably to break up the cruise to and from Barbados. It felt like the ship was moving pretty quick on those two nights.) I also flew in on embarkation day and with I hadn't. Puerto Rico is a US Territory so there are no required vaccinations or visa requirements. Remember there is also much more to PR
than the city of San Juan. It's great you are doing your research, I'm sure you can find plenty to do. But rain does put a damper on any vacation day.
Dominica was my favorite island, St. Martin was a close second. We enjoyed both for entirely different reasons.