You're animatedly welcome.
The most important thing to do in New York as far as I'm concerned is to eat. A lot of large cities say they have a lot of international options. Hong Kong calls itself the food capital of the world, but it's nothing compared to New York. New York has every type of restaurant known to man. If you go to New York and don't eat a real New York pizza and bagel, you didn't go to New York. Every New Yorker will disagree on which place has the best pizza, but they'll all agree that New York pizza is better than anywhere else.
Another important thing for me is to see a show. It doesn't have to be on Broadway. In fact, there are a lot of great shows off Broadway. The Theater District also has a lot of great food there's a great sandwich place on W 45th but the hotels are more expensive.
The first time I went to New York, I tried to see all the usual sites Empire State Building, Times Square, SOL, Central Park and I went home without knowing anything about New York. You only learn about a place when you do what the locals do. Parisians don't go to the Eiffel Tower every day.
Still, some things are pretty impressive. The Statue of Liberty probably means more to Americans than to foreigners, but it's worth seeing. You'll never stay at a hotel near it anyway. If you stay in Battery Park, you might as well take the ferry.
Ellis Island is less important if none of your relatives ever went through. The Staten Island ferry is free and runs 24 hours. It doesn't go to Liberty Island, but it passes by and gives you great views of the Statue, harbor and the city.
The Empire State Building has great views of the city, but it's not essential to see unless you're at a hotel nearby.
Times Square can be skipped entirely unless you're at a hotel nearby. It's nothing but an overpriced tourist trap. Unless you're going to see a show, but then you can just go directly to the theater without hanging out with the pickpockets. However, if I were there now I'd go to M&Ms World, but that's only because I don't live in a place with M&Ms.
Central Park has a million things to see & do, but unless you stay at a hotel nearby, you might want to skip it. It's an enormous park and you'll never see it all anyway. Or maybe just pick a small piece of the park and explore that. I would go to Strawberry Fields and just look around that area. It's also pretty close to Fairway.