We really recommend typing whatever you're looking for into google maps and going there, unless you have a super cool Puerto Rican friend who is willing to show you the sights.
Isla Verde Beach
Carolina, 00979, Puerto Rico
This is purportedly the calmest beach on the north side of the island, and there are jet ski rentals available if you feel like you do not go fast enough.
Museo de Arte de Puerto Rico
299 Avenida José de Diego, San Juan, San Juan 00909, Puerto Rico
Art museum for artsy peoples (apparently there is a garden).
Snorkeling
Escambron Beach, San Juan
Tripadvisor says this tour is really good for seeing sea turtles which seems pretty cool.
Costco Wholesale
1185 Avenida 65 de Infantería, San Juan, San Juan 00924, Puerto Rico