The U.S. State Department issues no special travel advisories for the Commonwealth of Puerto Rico, the way it might for, say, the more troubled island of Jamaica. However, there are problems in Puerto Rico, especially muggings along San Juan's Condado and Isla Verde beaches. Auto theft and cars getting broken into are other major problems. Do not leave valuables in cars, even when the doors are locked.
Take precautions about leaving valuables on the beach, and exercise extreme care if you're searching for a remote beach where there's no one in sight. The only person lurking nearby might be someone not interested in surf and sand but a robber waiting to make off with your possessions.
Avoid wandering around the darkened and relatively deserted alleys and small streets of San Juan's Old City at night, especially a section called El Callejón, near the intersection of calles San Sebastián and Tanca. Be especially careful along the narrow alley that connects this intersection with Calle Norzagaray. The district attracts more drug dealers than any other spot in Puerto Rico.
But the Old City and other tourist areas are generally safe. Avoid the seaside ghetto known as La Perla and the Cementerio de San Juan at night.