There are a few historic battle forts on the coast of Old San Juan. You can explore most of the grounds without paying - look for hidden hiking trails along the water! Get a kite and fly it on the lawn, or set up a picnic. If you don't make it here, don't worry - you can see Castillo San Cristobol across the street from the rooftop of the wedding venue!
"Balnearios" are small local beaches along the coast. This one in a small town called Dorado is a perfect beach getaway. The water is crystal clear with rainbow fish, parking is free and easy, and there are lots of bars and restaurants in case you get thirsty! ~30 minutes from hotel
Dormant volcanoes heat water in this area, which has been made into small pools. They are believed to have healing properties! Locals call this "the fountain of youth," which explains why when Amanda went, it was mostly full of old men (just thought you deserved a heads up). ~1 hour 20 mins from hotel.
Puerto Rico hosts 3 out of 5 of the world's bioluminescent bays, which are areas with micro-organisms that glow in the dark! The company linked below is closest to the hotel and hosts nighttime kayak trips through these bays. Puertoricodaytrips.com has a moon calendar that can tell you the best time to go. Make reservations early because this books up! ~1 hour 20 minutes from hotel to Fajardo. (note: there are biobays in other parts of the island you can look into)
Puerto Rico has two "virgin islands" called Culebra and Vieques. For a day trip you can take a catamaran snorkel trip to Culebra, home of one of the world's most beautiful beaches called Playa Flamenco (~1 hour 30 mins from hotel to the boat dock in Fajardo). You can also fly to one of these islands and stay there if you are looking for an extended secluded getaway.
Want to take a stab at driving through the mountains? Roka Dura is a good restaurant with mountain views. Make it a day trip by first going to nearby Toro Verde park - you can hike the trails through jungle mountains or zipline through the forest via Toro Verde Adventure Park. ~1 hour 30 mins from hotel. Hint: honk as you come around tight turns to alert other drivers that you can't see.
Head to Ponce, a city in the south, where you can take a ferry to "Coffin Island" for beaches, short hikes, and snorkeling! Unlike most of the other islands, this is a desert island, so it is a unique landscape. The area where the boat docks, "La Guancha," has lots of tasty snacks when you get back. ~1 hour 45 mins from hotel.