The Belvedere Hotel was on Budd Road in Woodbourne, NY, (several miles from South Fallsburg). https://www.brown.edu/Research/Catskills_Institute/hotelsbungalows.shtml
You can google for images of the Belvedere

It later became the Haywire Ranch, (1960’s) where you could rent horses for trail rides. It was owned by the Pepper family. https://www.legacy.com/obituaries/recordonline/obituary.aspx?n=joan-pepper-cauthers&pid=96434084&fhid=5760

After that it became and remains a yoga retreat https://sivanandayogaranch.org/

Amy Cohen