Since I’ve been to New York City several times for business, I thought I’d pass along some tips.
If you’re in New York City for a week, I would highly recommend getting a 7-day Unlimited MetroCard ($29). A single ride is $2.50, so just two trips a day makes it worthwhile.
However, you can’t use an Unlimited card at the same subway station for 18 minutes. This can be a problem if you use a subway station entrance that allows you to go in only one direction, and you pick the wrong one. So instead of exiting and re-entering in the right entrance (which will lock you out), just get on the next train and go to a stop that lets you cross over. (I found this out the hard way; only the persistence of my traveling companion got us in.)
If you’re flying into JFK Airport, I recommend taking the AirTrain to Jamaica Station. Once you get to the station, you’ll see a set of fare gates and banks of MetroCard machines on either side. You’ll need to get a $5 MetroCard just to leave the AirTrain system, so you’ll have to buy that before the fare gates.
But you can’t buy a 7-day Unlimited MetroCard at either of those banks of machines. Instead, proceed to the subway station at Jamaica (which, by the way, is called Sutphin Boulevard–Archer Avenue–JFK Airport, not Jamaica) and buy a 7-day card at its machines. From there, you can take the subway (E line) all the way into Manhattan. It will take about an hour.
If you want to spend a bit more money to save time, you can also take the Long Island Rail Road from Jamaica to Penn Station in Manhattan, which takes 30 minutes. If it’s the weekend, buy a CityTicket for the LIRR, which only costs $3.75 (a regular ticket is $8.75, off-peak $6.25). You can buy LIRR tickets at the ticket machines before the fare gates at Jamaica.
Enjoy your trip!