Once in NYC, there are many ways to get yourself from one spot to another. I first saw the citibikes or something like it while in Israel, then London. Last time I was in New York I did take notice of the bicycle paths marked out on the streets and this past week I notice the row of citibikes.
The most expensive way to get around in the city is a Limo, I suppose, but let's start with the more reasonable; the taxi. Now this is well worth it if you are coming in with luggage. I find the subway system to be safe and generally quite entertaining. For $2.50 you can get yourself a ride almost anywhere. Subway art is worth taking notice of and often there are musicians that add to the ambience. As far as I know, you can use the same ticket for a connecting bus ride. I'm not sure about these bicycles and I'm not even sure I would want to try one. They are purposed for short runs, not more than 1/2 hour at a time, but seem pretty reasonable if you have to make a few runs a day.
No doubt, the very best way to move short distances around the city is to walk. Wont have to spend a cent and you might even loose something....like an inch around your waist.