I've lived in Chicago, Houston, Los Angeles and NYC. I have traveled extensively just about everywhere else worthwhile and I have to say Manhattan is the safest place I've ever lived. It's hard for somone to kill you when you have 20 other people on the same block as you at the same time 24 hours a day. I often take a walk at 4am and grab a bite at one of the many quality restaurants that are still open at that hour without a care in the world. The policemen are also pretty darn nice.
We don't even think about the terrorists. The truth is really that people in NY think about the terrorist threat 5 times less than people everywhere else. Kinda ironic huh?