Punta Arenas is excellent for a quiet picnic, some family-friendly snorkeling, and views of the mainland (note the wind farm) and El Yunque across the water. The sand here is not very broad, punctuated with coral outcroppings, but there are plenty of shade trees. Snorkeling reefs extend for miles and you can expect to have this place pretty much to yourself, except on summer weekends, when a lot of yachts out of Fajardo come here on day trips.
To get here, drive through the rapidly vanishing former Naval Ammunitions Facility and head west for about 20 minutes through pastoral landscapes and past herds of semi-wild horses. At the western tip of the island, the road turns to dirt and you can park in the clearings.