I have never done much world traveling myself, but even for domestic US cities I have found that most areas which many think are "dangerous" really are not that risky to visit. They may have high crime rates, even high violent crime rates, but most violent crimes happen between people already involved in criminal activity. Most murder victims knew their killers. As a tourist, you are mostly part of the background scenery as far as the vast majority of dangerous criminals are concerned.
Studies have shown that suburbanites are at a greater danger of dying in car crashes than inner-city dwellers are of being killed in a crime. Yet its the crimes that make the 11 o'clock news (in lurid detail), while the car crashes at most warrant a brief passing mention.