'Yalies' are students from Yale University.
Yale University is a private research university in New Haven, Connecticut. It is one of the eight northeastern institutions known collectively as the 'Ivy League' colleges which are renowned for their academic excellence, selectivity as regards student admissions, and their social elitism. Originally a men-only college, it began admitting women in 1969.
Yale, founded in 1701, has numerous distinguished alumni, including five presidents of the United States, which gives added bite to Doreen's remark that 'Yalies' are 'so stoo-pit'!
At the St. Regis roof dance it was, in fact, 'Yalies' who were provided by the Mademoiselle team to act as escorts to Sylvia Plath and the other guest editors.