I was born in New York City and remained a resident for over 55 years. I did not live in Manhattan but in a suburb.
Once when I was playing in a Bridge tournament in Mass. someone asked me how many times have you been mugged? I had to laugh.. I have never been mugged in New York and dont know anyone personally who has been.
Dont be afraid of visiting New York City. There are so many sights to see:
Empire State Building
The Twin Towers
Statue of Liberty
Central Park and Zoo
Museums ranging from the Museum of the American Indian, Museum of Modern Art, Guggenheim Museum, The Museum of New York City, Metropolitan Museum of Art, Museum of Natural History etc. I could go on all day since there are easily 50 different museums.
You will have your choice of any type of ethnic food and unbelievable theatre and shopping.
New York is surely the Big Apple and you should take a big bite.
Unfortunately the hotels in Manhattan are rather expensive but well worth the expense to have the experience.