I am booked on an NCL cruise which is basically the reverse of your cruise next month. We leave San Juan and end up in NYC. We took a cruise out of SJU a few years ago and ended up staying the night to see a little bit of Old San Juan. This time, we're getting in 3 days earlier so we can see a little more of the territory. We will be visiting the El Yunque Rainforest and the Bioluminescent Bay at Laguna Grande. We're staying at the Aloft which is right near the Pan American Pier that the Epic will leave from. We loved San Juan and I'm excited to see more of Puerto Rico.
FWIW, you will need passports. This is not a closed loop cruise and passports are absolutely required. A friend was all set to cruise with us but her passport had expired and she had already sent it in to be renewed. Her original TA mistakenly told her she could cruise on her driver's license but that was wrong, even if both ends are US ports.