One of the best deals in New York City is a Metro Card. http://www.mta.info/fares/
The NYC Metropolitan Transportation Authority (MTA) runs the subways, buses, Metro North and Long Island Railroad.
In NYC you can get on a bus and deposit the exact change into the fare box. If you ask the driver for a transfer, the driver will give you a Metro card that you can use to transfer to another city bus within two hours. For example you can take an uptown bus and then transfer to a crosstown bus for $2.50. Not a bad deal. You can also buy a one ride ticket at a subway station kiosk with a credit card, cash –dollars or coins.
Metro cards are an even better deal and start at $4.50 for a two ride card. The $10 card is a good deal for weekend visitors to the city. With this card you get an automatic free transfer between subways and buses and between buses. You can buy these cards at the newsstand at LaGuardia just outside baggage claim and you can get them at most stationery stores and in subway stations.
When our kids were very young, and we didn’t want to give them individual cards we would buy one card and swipe it once for each of us. This works in some cities, but not in NYC. The NYC Metro cards can’t be used again at the same subway station or the same bus route for at least 18 minutes. So if you are traveling with a friend or a family you will each need to purchase your own metro card. Here's the link to the MTA http://www.mta.info/
Taxi’s especially in NYC traffic at rush hour can be very expensive, and wouldn’t you rather spend money in a restaurant in Little Italy http://www.littleitalynyc.com/ or in the shops in Chinatown http://www.explorechinatown.com/GUI/Content.aspx-Page=Discover.htm For bus and subway information can be found on these links as well as lots of information on festivals, food, and walking tours.
Last fall Roger Wade editor of Price of Travel published a list of the cost of Single-ride public transportation prices in 80 tourist cities. Take a look and use this as you make your 2013 plans. http://www.priceoftravel.com/595/public-transportation-prices-in-80-worldwide-cities/