It’s easy but fairly pricey to take a taxi or limo in to NYC from JFK. If you want to save some money, AirTrain JFK will connect you with the Long Island Rail Road (LIRR) or with New York’s subway or bus system for a fraction of the cost ($5 or less, depending on which MetroCard you use). AirTrain JFK allows “small domestic animals in secure carriers” on board, as do the LIRR and NYC’s buses and subways.
AirTrain JFK will take you to Jamaica Station, where you can connect with the LIRR to Penn Station or with the E, J, and Z subway lines (as well as a number of bus lines); or to Howard Beach Station, where you can connect with the A subway line and the Q11 bus line. When road traffic is nasty, the AirTrain may even save you some time. What it will not do, however, is take you to or from Newark or La Guardia Airports — it serves JFK Airport only.
For other posts about traveling with dogs on public transit, take a look at Dog Jaunt’s handy guide!