I am a former New Yorker- Born and raised in Brooklyn. I can tell you this- unequivocally, New York City is a photographer's paradise- it has so many interesting people and places to photograph. You would have to go there, take up residence, and spend 10 years seeing and experiencing everything and you would never take all of it in.
Where you go, what you shoot, and how you do it is going to be your decision. Asking other folks may be helpful but it all depends on what INTERESTS YOU- people. culture, architecture, art, entertainment, history, landmarks, fashion, slums, stores, high finance, jazz, beaches, bridges, museums, photographic equipment retail stores, botanical gardens, the Bronx Zoo, churches, synagogues, mosques, Grant's Tomb, I can go on for days.
So, check out this link- it contains a description (with photos) of over 80 popular points of interest- take your pick and make a plan.
https://www.timeout.com/newyork/attractions/new-york-attractionsYes, if you venture under the Williamsburg Bridge near the edge of get East River, you may see rats the size of very large tomcats. There are a few neighborhoods where they are more cockroaches than people but most folks do not go there.
I can guarantee that you will have a great visit- enjoy the people, the diversity, the great food, and all the sights.
When I visit my old home town I reals that, these days, I am spinning at 33 1/3 RPM and NYC is spinning at 78! After a while, I speed up
All large urban centers have criminal elements. NYC and the entire Metropolitan Area are well-policed. Most tourists utilize common sense and are not going to visit a public toilet in a deserted subway station at two o'clock in the morning.
A guided tour is safe and will give you a good overview, that is if you have a limited time. If you like it, you can visit again and concentrate on whatever interests you.