I assume by New York you mean New York City. I grew up in New York, but have only been to New York
City a handful of times. (It's like telling someone you live in Texas and they say "what part of Houston"?)
Street photography is always a hoot. There are lots of museums. Most will allow cameras without flash. Take a Circle line boat tour from Southstreet Seaport. Fulton Fish Market is nearby. Subways are good subjects. (they can be underground or above ground). Grand Central and Penn Station are photogenic. Lots of colorful opportunities in Times Square. View from the top of Empire State building. New York library. Central Park. Thousands of taxis in Manhattan. Visit Soho and see the galleries and boutiques.
Hell's Kitchen for dining.
The quickest way to tell a tourist is that they are walking slowly and looking up at the tall buildings. Eye contact with others is minimal, especially if they look even a little weird.
If you carry your camera, keep a tight grip on it. I've carried my 30D and large lenses around everywhere without incident. I also don't go into unfamiliar neighborhoods and don't travel alone after dark. I weigh in around 300 lbs. and have an intimidation advantage. I don't press my luck.
You'll have fun,,,,,,,, if you survive.......
