American Tourist Murdered in Antigua

Another tourist murder mystery has come out of the Caribbean. Last week, a young San Francisco woman was killed during a cruise stopover on the island of Antigua.

Many questions remain in the stabbing death of Nina Nilssen, CBS News correspondent Michelle Miller reports. The 29-year-old aspiring composer-musician was found dead last Tuesday near Pidgeons Point Beach, a popular destination on Antigua.

How to Protect Yourself in Paradise

Nilssen was part of a wedding party on the cruise. Some member of the party had gotten off their cruise ship, the Royal Clipper, for a barbecue. Nilssen disappeared, but was later discovered on a trail not far from the celebration. She'd been stabbed once in the neck.

Etai Freedman, one of Nilssen's friends, told CBS News, "Nina had no ego. She was in touch with people on all levels of life. She gave everybody her time."

Nilssen is the fourth tourist murdered on the tiny island since 2008. In July 2008, British honeymooners Ben and Catherine Mullany were shot in their hotel room. And last January, Drew Gollan, a 38-year old Australian yachtsman, was shot in the chest. Police believe robbery was the motive in all three homicides.

Crimes against tourists have made news recently in other Caribbean nations, as well. High school senior Natalee Holloway vanished on spring break in Aruba in 2005, and in 2006, CBS News employee Ryan Smith was viciously attacked in St. Maarten.

Security experts advise that, even when in paradise, vacationers should be on guard.

Tim Horner, of Kroll, a risk consulting company, told CBS News, "Even if it's sunny outside, doesn't mean it's a low-risk or a low-crime area, and you have to pay attention."

Nilssen's killer is still at large.