Vehicles out of NYC are more expensive than taking a bus to Kingston (10 mins. away from Woodstock), or Amtrak to Poughkeepsie (45 mins. away from Woodstock) and renting there. Most car companies will shuttle you to/from their locations from to/from your transportation. If you are returning on Sunday, they will usually be closed and will not have shuttle service to your train or bus, so if you take this option, be sure to ask 1) if they have a Sunday drop box for your keys for Sunday returns and 2) taxi number for a ride from drop off place to your bus or train on Sundays for closed hour drop offs.
Google: Kingston car rental companies, Poughkeepsie car rental companies and Taxi services (booking in advance recommended):
About 2 hours from the city. Trailways (trailwaysny.com) is the major bus line from NYC to Woodstock or Saugerties with frequent departures. The Woodstock and Saugerties stops are equidistant from the barn (10 mins) and Kingston has more frequent arrivals/departures (20 mins).
Two options by train:
Amtrak - 1.5 hrs from New York Penn Station to Rhinecliff. From the station, it's about a 25-minute drive to Barn on the Pond.
MTA Metro-North Railroad (Hudson Line) - 1.5 hrs from New York Grand Central Terminal to Poughkeepsie. From the station, it's about a 50-minute drive to Barn on the Pond.
Both trains take you on a beautiful, scenic trip up the Hudson River.