Sarah Berkes was delighted, if also very surprised, to find that a place like the Webster Apartments on West 34th Street still existed in New York City. The stately rooming house for “career minded professional women” where she has lived for a little over a year is one of the few of its kind left in the city.

Ms. Berkes had wanted to work in fashion her entire life, so she was ecstatic when, last November, five months after graduating from the University of Washington, she got a job offer from a sportswear company in Midtown. Her enthusiasm was tempered only by the facts that it was a Friday, they wanted her to start on Monday, and she was living with her grandparents in Belvidere, N.J., a two-and-a-half-hour commute to Manhattan.

When Ms. Berkes stopped to share her good news — and predicament — with a friend, the friend’s receptionist recommended she check out the Webster Apartments, where she had lived during an internship the previous year.