New York in 4 days

For me exploring a city is all about understanding how the local people relate to, and live in, that city. If you have a similar interest, then a surprising lot can be achieved in 4-5 days - provided of course you start the day early and end the day late, and go back to the hotel room only at night merely to sleep.  Essentially what I did in 4 full days (and 5 nights) - and which I would recommend any tourist visiting New York - is the following:

1. took some time off to understand the subway system (the metro) - how it works - how to connect etc.  The New York Metro is a great boon to a tourist - safe and affordable - though it can be confusing at times.
2. walk the streets - especially the streets that I had heard and read much about - 5th Avenue, Broadway, Park Avenue, Madison Avenue
3. Explore Central Park - I went there on 3 days and spent a couple of hours each day exploring different corners of the huge 850 acre Park - both on foot and on a rented bicycle, and ogled at the swank buildings & apartments over-looking Central Park.
4. New York is synonymous with Broadway - so see at least one play/musical on Broadway (I saw "Phantom of the Opera" - one of the longest running plays on Broadway).  Buy tickets on Times Square at a steep discount on the day of the show. 
5. visit the famous districts such as Greenwich village, Meat-Packing district, Washington Square, Sheridan square - all of which have a marvelous atmosphere, and are excellent for walking
6. spend a couple of evenings hopping across various jazz clubs/pubs near Sheridan square - and enjoying the different jazs jamming sessions which go on till late in the night
7. go on a very relaxing cruise to Staten Island using the free Public ferry service from Battery park - and in that process see the Statue of Liberty (from a distance), and the Manhattan skyline
8. explore certain "living" land-marks and do some "serious people watching " at places such as the Grand Central, Penn station & Times Square
9. Visit the 2 museums worth visiting : Museum of Modern Art and American Museum of Natural History  
10. take a walk on the High Line - the resurrected over-head rail line now converted into a mile long green park
11. explore the financial district on foot, and see the venerable buildings that have featured in many a movie about life on Wall Street
12. and - totally optionally - try to visit a night club to understand how the upper crust of New York (with money to burn) spend their evenings.

I also briefly saw (from the outside) - the Rockefeller tower, the Empire State Building, and the site of the WTC where the new "Freedom Towers" is almost ready.  I did not spend much time on these Buildings, and did not spend the small fortune required to enter the viewing galleries on those buildings.

And of course, if, like me, you have never ever experienced snow, then Central Park in New York is the best place to do so.

Alas, I am not much of a foodie - so I did not explore the many cafe's and restaurants that abound all over mid-town New York. For a foodie, New York is paradise - and I suspect I missed out on one of the most crucial aspects about New York because of my limited gastronomical interests.