A couple of years ago we decided to do New York City for a holiday. I had a preconception about NYC from TV shows, in that it was this crime riddled place where I wouldn't feel safe. Well... I can dispense that myth, in that NYC is one of the safest cities I have ever visited.
My wife and I walked around the city until early hours of the morning. On near every corner there is a police car and cops at the ready. Basically, the city took steps to simply stamp out crime by blanketing police across the city so those thinking about committing crime, think twice before they bother. It would be near impossible to get away with it due to the police coverage. Sure, crime still happens in NYC, no doubt about it... but in general for a tourist, the city is good to go for getting yourself around.