Locals will tell you the island is split into a violent and often dangerous east and a laid-back and welcoming west.
While most of the violence is likely to befall locals involved in the island's heavy drug trade or gang activity, tourists are sometimes unfortunate bystanders or targets of serious crimes.
One particularly heinous incident involving a tourist occurred in 2009. An American woman visiting from the state of Georgia was abducted while jogging in the marina area of Fajardo. She was stuffed into the trunk of the perpetrator's car and later found dead with her throat slit. She was five months pregnant.
Don't be caught out at the wrong place and the wrong time. While incidents like these and other violent crimes are rare, there are some areas in which to be particularly cautious and others to just stay out of all together. Criminals in these areas may walk the streets looking to mug people, and drug activity is common at night.
Many travelers say to avoid La Perla in Old San Juan, next to El Morro, which has a high rate of drug trafficking. Another travel writer said Santurce in the same city can be dangerous.
The areas of Puerta de Tierra outside the hotel hub should also be avoided due to large amounts of drug activity and other criminal behavior. Stay out of Parque de las Palomas, a park area in San Juan, after dark.
Ponce, in the south part of Puerto Rico, is another location in which to be vigilant. And at night, beach areas may attract those with sinister intentions like robbery or rape.
Travelers say to avoid public housing areas, known in Puerto Rico as "caserios", identifiable by their cement facades and apartment-like balconies. Gangs are a problem in these projects, and activities linked to the drug trade take place often.
One of the worst caserios in San Juan is Louis Lloren Torres. This is where a lot of the city's crime takes place. It's off the tourist track, so travelers may have a death wish if they end up there.
While any crimes involving weapons are most likely to occur between local criminals and people in the drug trade, visitors should be aware of Puerto Rico's high rate of gun deaths per capita. Accidental shootings also occur, sometimes due to the Puerto Rican custom of firing guns to ring in the New Year.
Shootings and knifings have also occurred on buses operating late at night outside San Juan.
Some travelers suggest getting in and out of the major cities as quickly as possible and spending more time exploring smaller towns on the island with lower or relatively nonexistent crime rates. Guayama is one recommended locale.
Nomads who've commented below have other suggestions for safe and beautiful destinations within the country. Get out there and enjoy.