We booked everything in advance and paid for fast track when possible and it was the best we could have done.
Empire State for example - we walked straight in, up, were treated like royalty, enjoyed the views, down again. All done within an hour. The queue for people without fast track tickets was over three hours! I didn't want to waste precious time we had there queuing.
Same for other attractions like ice skating, Madam Tussaud's or the American Museum of Natural History, just straight through while others had been waiting outside for hours. Ok, we went at New Year's, so definite peak season, but I reckon New York is always pretty full.
To see the Statue of Liberty - don't be fobbed by the people who sell tickets on the streets in the area. You can see it for free (unless you are desperate to go in/on it). The ferry to Staten Island runs every half hour and is the only thing that's for free in New York. You just walk on, get great views of the SoL, then get straight back (or stay on Staten Island if you wish for a bit).
Foodwise - I loved all the street vendours. Falafel, kebabs, doughnuts, hotdogs... Pizza is the best there. And don't forget to have a cheescake!