Actually…if you can go to Culebra, an island near Vieques, you can find some excellent unspoiled beaches. Vieques has them too, but like Chrome says, it’s not exactly tourist destination right now.
Also, in Isla Verde, there is the Balneario de Carolina, a public beach with some things like bathrooms and gazebos. Or you can try any other beach of the area.
Please, if you can LEAVE THE METRO AREA!!! Search for information on the natural reserves that we have. For example, the tropical rain forest of El Yunque, the Faro de Fajardo and Cabezas de San Juan, La Parguera, and Cuevas de Camuy.
El Yunque is located in Luquillo. It is also a mountain (well, a small mountain) and part of the Cordillera Central, a chain of mountains that divide the island between north and south. I do not know if right now they let the people climb to the top, but if you can, do it. It is a good experience.
Faro de Fajardo and Cabezas de San Juan are located in (surprise!) Fajardo. The Faro is one of the best kept we have, and it houses a museum of tropical marine life. The are in which it is located, Cabezas de San Juan, is a mangrove haven. They give tours through it, showing the different species of flora and fauna.
La Parguera is in Cabo Rojo, in the southwest part of the island. It is one of the three areas in Puerto Rico where we have biolumiscence seas. Unfortunately, pollution has taken its toll in the fragile ecosystem, so the bioluminiscence is not as notable as it was before. That are also has mangroves, and if you can find a way to see them, well…good for you. During the day there are booths that sell local food. (BTW, another biolumiscence beach is found in Culebra)
Cuevas de Camuy are located in (surprise again!) Camuy. That is in the northern part of the island. It consist of a system of caves and also of the vegetation(forest?) that surrounds it. I think tours are given. From what little I remember of school trips, it also is the home of some unique spieces of microorganism.
If you do not want to go so far, well…you can go to Jardín Botánico in Río Piedras. It is a botanical garden attended by the University of Puerto Rico.
My advice? Rent a car, buy a map, and ask for the telephones number of the (government, in many cases) agencies that are in charge of those places. See if they answer your questions (any questions). If they offer tours, arrange your trips and go!