Hey Purza
New York is TOO big to do in one weekend.
See Central Park ( good weather only); have a grand lunch in the Palm Court at the Plaza Hotel on 5th Ave and the Park. Go to the Metropolitan Museum of Art and have lunch in their stunning cafeteria. Check out all the neighborhoods at the upper west side.
See a concert at Lincoln Center ( outdoors in the warmer months or indoors) on the upper west side.
Go to Battery Park; the South street Seaport; window shop along upper Madison Ave.
It is an overwhelming city and its height and breadth is dizzying. You do need time.
If you will be on Long Island; take the Robert Moses Causeway south to Fire Island; a barrier island to the Atlantic Ocean. Go to parking field 5 and you can walk to and walk into and tour the Fire Island Lighthouse. We have done it and it is fun. It is a traditional old lighthouse and I believe it is still in use. It was used in the movie "Men in Black 2".
Also, if you want to drive out to Montauk, there is the famous light house on that point.
Have fun! Frank