You wouldn't be saying this if you were a person of color living in the Bronx or parts of Brooklyn, because things have gotten worse for those folks due to policies of selectively enforcing vice laws and programs like stop and frisk that have become popular under Guilliani and Bloomberg.
Of course, why crime rates have generally fallen over the last couple of decades in cities like NYC isn't well understood and no one person or administration can claim that they are responsible. However, we do know that NYPD policies are enforced in a way that promotes racism and class disparity and that Bloomberg has been a supporter of those policies.
It is important to realize that a benevolent dictator doesn't really exist and having balance in government is necessary, otherwise the people who do get shafted by any given administration get even less of a voice and support.
Those neighborhoods are where crime happens. A map of violent crime in Chicago (a city that's 65% black or hispanic): http://upload.wikimedia.org/wikipedia/commons/2/29/Chicago_v....
A map of Chicago by race: http://www.radicalcartography.net/index.html?chicagodots
What do you want the police to do, patrol around Lincoln Park and Lakeview where all the wealthy white people are?
No, but city and state gov't should be responsive to the causes of these issues and be proactive about solving them. Usually that will mean looking at class and race disparity and implementing policy that will provide better opportunities for those people, as well as defeating existing roadblocks that prevent those people from taking control of their lives.