Visiting NYC and what to do there really depends on how much money you have to spend. Lodging in the city is expensive, but something one should do once in their life time, especially if you want to take in any Broadway show which also is expensive, although matinees are less expensive, again being a once in a life time experience.
Less expensive things to do would be visiting some of the museums, Rockefeller Center, Radio City Music Hall, Katz's Deli, South Side Sea port. Soho is also a good place to visit as is the Empire Sate Building, The Statue of Liberty, The U N Building and a Cruise up the Hudson. Of course this all depends on how long you plan to stay as well.
If your stay is just over night and you are on a tight budget I would suggest: plan on visiting the Statue of Liberty, The Empire State building, the U N and the South Side sea port. In the evening you can have dinner at Katz's Deli, see a show at Radio City Music Hall then go across the street for Ice Cream at Schraffts in Rockefeller center. Cental Park is also a nice place to visit during the day but stay out of the park at night.
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