Here is an itenary for New York city if you have only one day there.
1) If you are arriving by train or bus you will arrive at the Central station/Port authority bus terminal (Lets say by 11AM). If you come by car, park it somewhere near there for the whole day. (Don’t try to drive around the city for sightseeing. You will spend the whole day finding directions and parking space). First of all buy a tourist map of the city (about 2$). Go underground and get on the subway and go to the World Trade center stop. Get out and look at the site.
2) Using the map, walk to the battery park (the southernmost tip of Manhattan)(12noon). Buy your tickets for statue of liberty and take the ferry. Spend about 3 hours on the whole trip and be back at battery park by 3PM
3) Use the map again and walk towards Wall street/New York stock exchange. Grab something to eat on the way. (4PM)
4) Take a subway from around Wall street and go to the Empire state building. Get in the line and go up. Spend about an hour for the whole thing (6PM)
5) Walk towards the broadway/Times square. By the time you reach there (about 15 minutes) it will be dark and you can see the Times Square in all it’s neon glory. Do some souvenier shopping here. (7PM)
6) Its time to walk back to the train/bus/car.
There is much more to see if you have more time. One tip-if you have the time and really want to experience the city, not only the touristy sites, walk from battery park all the way to the times square. For me it took nearly 4 hours plus time to eat and relax on the way. It is really worth it and you will cherish that walk for a long time.
Happy sightseeing!!