Because of the high level of hygiene in the US, infectious diseases will not be a significant concern for most travellers. The high cost of medical care could leave you feeling a little poorly though.
Many, many out-of-towners still expect to visit here and find the New York of the 70s - all graffiti-stained subway cars and menacing muggers - but ex-mayor Giuliani's radical cleanup of the city has had startling effects. The murder rate has come down 69% since the early 90s. Times Square and the famous 42nd Street thoroughfare continues to evolve into a brightly-lit, family-friendly circus. Even the least savvy, most wide-eyed tourists ride the subways at night, encouraged by primped signage and immaculate new subway cars, and it's nearly impossible to find a Manhattan neighbourhood that's off-limits after dark these days.
That said, New York is still a big city, and one in which the gulf between have and have-not yawns ever wider. Sensible precautions against pickpockets and scammers still apply, and it's wiser not to roam around at night until you have a feel for the area.