You have a few options for exploring the waters. You can snorkel at Playa Escambrón in Old San Juan without needing a boat. Alternatively, you can take a catamaran trip to Culebra or Vieques.
Make a stop at El Yunque National Forest and take a hike through the rainforest, which is managed by the U.S. Forest Service. Be sure to bring a raincoat in case it rains. Additionally, avoid entering rivers if it has been raining in the mountains due to the risk of flash floods, and always follow safety guidelines.
Visit a local panadería for breakfast.
Enjoy some river caving adventures. There are more than one touring company that gives this experience in Utuado. I did this in 2016, using Caribe Adventures Puerto Rico. Other websites have options to provide transportation from Dorado (closer to San Juan) https://www.viator.com/tours/San-Juan/Tanama-Waterfalls-River-Tubing-Adventure/d903-57869P10#:~:text=Pickup%20point,will%20be%20at%208:00am
The “Ruta del Lechón” is in a mountain area called Guavate in the town of Cayey. The road includes multiple business called “lechoneras”. Weekends are great day to visit this zone to taste some suckling pig on the stick. Some businesses will have live music and good local ambience. We visited El Rancho Original, had some pork and drank some Maví (a tree bark-based beverage grown, and widely consumed, in the Caribbean).
Faro is spanish for lighthouse. Visit the southwest of Puerto Rico, Cabo Rojo is famous for their salt flats, the lighthouse, their clear water beaches, and the region of Boquerón. We hiked the Faro los Morillos Trail, and stayed at Boquerón on one of our trips. On our way out we stopped at Yauco (town known for their coffee plantations) and had brunch at Dolche Salao.
A place to find things to eat and drink, shop or other entertainment.