NYC is one of the safest, if not THE safest large cities in the U.S. - I want to address some important Brooklyn facts before people absorb crime stats for this ONE borough of New York City. The link at the bottom gives you a precinct by precinct, borough by borough - MONTHLY and yearly perspective on crime in NYC.
Brooklyn, on it's own, without the other 4 boroughs would be one of the top 5 largest cities in the COUNTRY. Brooklyn, ALONE, has 2.5 million residents. This is not counting illegals, and those not counted by the last census. Brooklyn, is HUGE, just look at the map for NYC and look at the breadth/width of Brooklyn compared to the other boroughs, it is also densely populated.
Brooklyn also has an AMAZINGLY diverse Real Estate market - Coops, Condos, Lofts, Brownstones, Detached Mansions, Ranch, Victorian homes from the early 1800's, and more. Price ranges in Brooklyn go from the low mid 400's to the Millions, and neighborhoods are as unique as the people that live in the city. Is Brooklyn safe? It is as safe as Manhattan is, or any other borough. And just like any other borough or Manhattan, at night certain areas are less savory than others - at night. Even the Upper East Side of Manhattan, where you find multi-million dollar apartments, had a rapist terrorizing women for years. So, do not look at Brooklyn as being any more unsafe than any other NYC borough. It truly is a case by case, block by block issue for anywhere in NYC.