First, ignore everyone telling you to stay away. Yes, NYC isn't as great as she was, and the advice about situational awareness is spot-on. But she's not Detroit yet.
If you're religious, St Patrick's is worth the visit. If you're Catholic, I recommend St Agnes or The Church of St Michael.
One of my most favorite places in NYC is Bleecker St. There are lots of music venues and clubs. If that's not your style, at least visit Thompson St near Bleecker...perhaps the coolest chess store in the Universe is there.
Everyone recommending that you get a slice of pizza is right...but I'd go further and recommend getting pork fried rice from any dive Chinese restaurant (provided you're not on a restrictive diet).
Finally. I'd recommend MoMA over the Met. And keep your wallet in your front pocket. And leave your gun at home.
Yes, I would still recommend NYC as a good place to visit. In fact, with the crowds down somewhat and the weather finally starting to warm up, it's an ideal place to visit.
Lot of great suggestions on the thread already. I would make sure Grand Central is included, it's really worth checking out.
Definitely walk the Brooklyn Bridge. Also take the Staten Island Ferry. It will give you a great view of the Statue of Liberty without having to actually go there (which is not worth the money in my opinion). The Staten Island Ferry is FREE so do not buy tickets from scamsters trying to sell you tickets to it. Just ride to Staten Island, look around a bit and get on the next ferry back.
There will be scamsters trying to sell tickets on the street for things like Empire State Building, Statue of Liberty, etc. The people selling them will look official too, with uniforms and such. Never buy tickets that way. They are a ripoff and you will go to the back of the line like everybody else, despite what they tell you.
The fear of crime in NYC is greatly exaggerated by people who just don't know the city. It is extremely safe here, especially in Manhattan south of say 110th Street. Though you can go to any of the boroughs (to the commercial areas) with no hassle. Just stay out of the residential areas, especially those with housing projects. You will definitely stick out and be watched. I only go there when I have business there and then I get right back out. Brownsville and East New York (Brooklyn), for example, are no-go zones but there's nothing for a tourist to see there anyhow.
The subways are getting sketchy - I would stick to ground transportation. Also, it can be tricky for a tourist to learn the subway. If you do get on it though, know that uptown will take you north and then usually to Bronx and/or Queens and downtown will take you south and eventually into Brooklyn (as a general rule). Do use Taxis and Ubers if it is too far to walk.
Plan on a lot of walking in Manhattan. While it looks small on a map, it's deceivingly big. Figure a mile for every 20 blocks (going north/south) and about a mile every 6-8 blocks going east/west) as those blocks are typically much wider. So make sure you have comfortable shoes. Nobody cares what shoes you wear. Even when I wear a suit, I'm wearing sneaker type shoes.
Eat at the local restaurants. Avoid the chain restaurants that you can eat at anywhere. The food trucks are generally amazing but stay away from food on the carts, especially around Times Square.
Absolutely see Central Park and plan to spend at least half a day there. I do not recommend the horse drawn carriages you will see at the bottom of it (59th Street) - way overpriced.
Stay out of the various "gift" shops, they are a rip-off and if you don't want to stick out like a tourist, never wear that "I Love NY" clothing with the hearts on them and things like that. You want to look like a local so you are less of a target (for the scam artists). The scam artists are harmless if you just avoid eye contact and walk right past them and pretend you are not hearing or understanding them as they try to get your attention.
You will see a lot of homeless people and panhandlers. Some of them can get aggressive about asking for a handout, especially if you make eye contact. Don't let them tug at your heartstrings. Trust me, you are not helping them by giving them your loose change. Just keep on walking and they will move to their next target.
Also be aware of the well dressed people who usually hang out at Penn Station, Grand Central or the bus terminal giving you a sob story of how they had their wallet stolen and need train/bus fare home. That is 100% a scam.
Don't feed the pigeons either!
New Yorkers can come across as cold and heartless but we are actually quite friendly and happy to help tourists find their way around. The NYPD are especially very friendly and approachable so don't be afraid to ask them for directions if you are lost. You can also ask well dressed businesspeople types but also don't be offended if some of them blow right by you - some of us need to make a train or an appointment somewhere.
Hope you have a great time.