We have done several
DCL sailings to and from San Juan. We love PR.
If you plan on staying just in San Juan, Uber works well from the airport and to the pier as well as in town. The city is very walkable, but like any city anywhere, be aware of your surroundings.
We have stayed near the edge of the Carolina area, and had plenty of shops and restaurants available. The bio bay by Fajardo was an excellent suggestion. Check the moon phase, and hope you are there when you're as close to the new (no) moon put, the darker the night the better. If you're not certain about kayaking, there are one or two suppliers that bring you in with an electric powered boat. Very relaxing. Not sure about ubering out there, we drive. You can also take a ferry out to Vieques.
But, we prefer getting away from the city, and utilized rental cars. We've stayed out towards the Luquillo area, not far from El Yunque, the rainforest. A drive up into the rainforest, with a few short stops to hike in a bit, or even for a dip in a waterfall, is a great experience. Also out that way, look into la Ruta de lechon, and stop at Los Pinos. Lechon is roasted pork, and I can't describe how delicious a meal you will have, with a frosty cerveza.
You can go to the kioskos closer to San Juan in Loiza, but a little further out is the kioskos of Luquillo, a row of probably 50 or so varied establishments. Beer from one, shrimp from the next, etc., The sunset from the far end restaurant is beautiful.
Enjoy your time there.