Broadalbin is the name of both a town and a village in upstate New York, which derived their names from Breadalbane in Scotland. Whether there is/was a real hotel of the name in New York City is unknown, but its use would seem to derive from Robert W. Chambers having had a summer home in Broadalbin, dying there.
Broadalbin, by way of Breadalbane, derives from Scottish Gaelic Bràghad Albainn meaning "the upper part of Alba". Alba (Scotland, or, historically, Britain as a whole) is ultimately based on the Indo-European root for "white". Hence Broadalbin could be taken to mean "the upper part of white" or "white upper part".