To get from JFK Airport to Fishkill, you can take a combination of public event transportation NYC or a taxi/rideshare.
One option is to take the AirTrain from JFK to Jamaica Station, then transfer to the Long Island Rail Road (LIRR) to get to Poughkeepsie. From Poughkeepsie, you can take a taxi or rideshare to Fishkill, which is about a 15-minute drive away. Alternatively, event transportation NYC you can rent a car or book a direct shuttle service for convenience.