What's the closest hospital to Briarcliff Manor and is it any good?

Phelps Memorial Hospital is just southwest of the village. It has state of the art facilities, including a hypebaric chamber ideal for healing wounds and carbon monoxide poisoning. It also is a Memorial Sloan-Kettering Cancer Center for the convenience of the Westchester County residents. It is among the leaders in hip and knee replacement, and their emergency room is open 24/7, receiving ambulances from all the neighboring towns.
Having raised a family in Briarcliff Manor, have been there repeatedly for different issues, and always received the best of care.

Westchester county has 12 hospitals, none more than 30 minutes from Briarcliff.
see http://www.thirdage.com/d/h/westchester-county-hospitals-ny

In addition to Phelps and Westchester Medical Center mentioned above, Northern Westchester Hospital in Mount Kisco is also well rated and near-by.

Phelps Memorial in Sleepy Hollow and Westchester Medical Center in Valhalla are both around 15 minutes drive from the center of Briarcliff Manor. They are both well regarded hospitals and are seen are reliable for emergency care situations. For non-emergency medical conditions, it may be worth doing some research to assess specialization ratings and recommendations.