A complex question to answer because, as I told you, New York has a number of attractions that can be considered a truly impressive must.
So what not to miss depends on the days you have and your tastes of course.
I always advise against combining a visit to New York with too many other things, Niagara Falls are interesting and there are many beautiful cities not far away (see Philadelphia, Boston, Washington, Annapolis, …) but try to leave at least 6-7 days for New York, if you can.
Seven full days would already allow you to have a good overview of the city, you will visit the essentials without too much haste.
Starting from Manhattan, the borough with the most things to visit, I would say that the financial district with Wall Street and the New World Trade Center are unmissable, perhaps combining a visit to Liberty Island (where there is the Statue of Liberty) on the same day. and Ellis Island. Do not believe those who say that to visit the statue you just have to pass by with a boat!
Going up north you will encounter unmissable areas such as Soho, excellent for walking, shopping and admiring older and more human-sized architecture. Those who love the most multi-ethnic soul of the city cannot forget to wander through the East Village where many different cultures meet.
Greenwich Village is also wonderful, a residential and quiet area animated only by the presence of the famous New York University: stop on one of the benches in Washington Square Park.
Certainly not beautiful but still with a story to tell are Chinatown and Little Italy, where the first has literally surmounted the other, now reduced to little more than a street (Mulberry Street). Today one of the few and true Indian communities in New York is the Bronx, at Arthur Avenue.
Chelsea, its Art Galleries and above all the wonderful High Line park are absolutely unmissable: don’t forget to pop into Chelsea Market for a quick lunch.
Going further north, don’t forget a postcard photo at the Flatiron Building, the very particular building in the shape of an iron. A little further north begins Midtown with its thousand attractions, from the Empire State Building, to Rockefeller Center to Times Square.
Spend at least half a day in Central Park, at least its southern portion if you don’t have time to do it all. And don’t forget to plan some of the museums, there are lots of high-level ones. Metropolitan, the American Museum of Natural History, , the 9/11 Memorial & Museum, the Collection and much more.
Moving on to Brooklyn I recommend a nice walk on the Brooklyn Heights Promenade, some photos of the Brooklyn Bridge from the Empire Fulton Ferry park and then cross the bridge towards Manhattan.
You will have understood that I could go on for hours and have not mentioned anything about Queens and other parts of Brooklyn that are worth a visit (as well as Staten Island, Harlem and Morning side Heights). My purpose was just to make you understand how many beautiful things there are to see: it’s up to you to make the selection!
The Top of New York City:
I do not like the rankings, also because it is not easy to clearly identify the attractions that can be considered “unmissable”, everyone will find their New York but I would still like to try to collect a series of “things not to be missed”. I will avoid being too alternative and try to focus on the attractions that are really appreciated by those who go for the first time. Consult Immigration Here for Visa
Statue of Liberty:
Symbol of the city and the entire nation, do not miss a visit to Liberty Island for anything in the world. Do not listen to those who say that seeing it from some boat is the same thing: you have to take the State Cruises ferry and also visit Ellis Island and its touching museum on immigration.
Top of the Rock:
Years pass and new dizzying observatories emerge (such as that of the One World Trade Center) but the Top of The Rock is always the best because it is optimally positioned in Midtown.
Going before dark you can see all of Central Park (to the north) and Midtown of Manhattan (to the south), with a splendid view of the beautiful Empire State Building.