How to get here from JFK or New York City
It is very easy to get to the Hudson Vally from New York City or JFK without a car. You will not need a car at Beacon, Cold Spring, Poughkeepsie (Walk Way over the Hudson) or Peekskill.
The Walkway over the Hudson elevator is Seasonable. So if you go in the winter you might need a very short cab or uber ride.
From JFK:
Take the airtram at the JFK airport to Jamaica Station which is a major rail hub in Queens New York City. The Airtram is also used to get to hotels and car rental locations. You will find at Jamaica Stations trains that go to Penn Station, Grand Central Station, Brooklyn, and Long Island. Use the TrainTime App for tickets. To exit the AirTram tap your credit card using your phone. The LIRR trains run all the time.
For the Hudson Valley you want to go to Grand Central Station.
They recently built a beautiful new Long Island Railroad terminal in the bottom of Grand Central. I think it is the cleanest location in NYC.
When you get off the train at Grand Central take the escalators up to the main terminal of the LIRR. Take a left and follow the signs to Grand Central Terminal.
Take the Hudson Line which will have Poughkeepsie as your final destination.
The train stops at multiple locations but I suggest Cold Spring, Beacon, or Poughkeepsie (Walkway over the Hudson).