Fly into JFK, LaGuardia or Newark. All three connect to a train, so skip the rental car.
JFK (Delta, JetBlue, American): the AirTrain runs to Jamaica for the LIRR and the E, J and Z trains, or to Howard Beach for the A train.
LaGuardia (Delta, American): no rail link, so take the free Q70 LaGuardia Link bus to the subway at Jackson Heights, or ride one more stop to Woodside for the LIRR.
Newark (the United hub): NJ Transit and Amtrak stop at the airport's rail station.
NJ Transit, Metro-North, the LIRR and PATH all run into the City from the suburbs.
October here means highs in the 60s and cooler nights, so pack layers and a light jacket for the walk to and from the train. If you can stay an extra day, the leaves in the Hudson Valley usually peak around mid-October.