We arrived about the same time you do. We just went right to the ship. However, if you return to San Juan at the end of the cruise, maybe you will have time then to do an excursion. We did the Forts then. Depending on what time your plane leaves, you may even have time to do the Rain Forest which I understand is a "must see". I think that even if the ship doesn't leave until midnight, you have to be on by a certain time.....but, I'm not sure about that.
We just used that time the first day to rest up, get to know the ship, etc. We ate dinner on the ship that night.