I have been twice to NYC as part of New England tours, I went last September and did the add in to spend more time doing my own thing!! So many things to do and see. It does depend on what you like!
Most recent time I went over to see Statue of Libery and Ellis Island well worth doing, I also got the train to Central park and went on a horse drawn carriage ride very nice, went the the 9/11 memorial and museum I pre booked a audio and guide tour learnt so much. many museums churches and shops. time before Empire State, theatre queued to get cheaper tickets, shopping, etc.
There is so much to see and do if you have spare time pre book things then you won't waste time queuing any other questions just ask.. Have fun and enjoy yourself!
Cindy