The story
The main corridor connecting the two buildings comprising the Waldorf–Astoria was given this nickname by the press in New York City in reference to wealthy patrons (especially women) who would go there to show off their finery (compare peacock (“strut proudly”)). The name then came to refer generically to the foyer of any such upper-class hotel, or similar gathering place. First appears c. 1904 in Real New York by Rupert Hughes.
Etymology from Wiktionary, CC BY-SA 4.0.