Amtrak trains stop at Rhinecliff, NY. Shortline buses stop in Rhinebeck, NY. 
Taxis are often waiting at the train station, a 5 minute ride away but less available in town for bus arrival.
Shortline Bus to down town Rhinebeck
https://web.coachusa.com/shortline/
Amtrak train to Rhinecliff Station
https://www.amtrak.com
Taxis:  845 - 532 - 5788
             845 - 876 - 2010