There are lots of places in the city that show independent and foreign films. But movie fanatics who lived in New York in the 50s, 60s, and 70s still bemoan the loss of certain legendary theaters, like Bleecker Street Cinema, which opened in 1962 and closed in 1990.
After ceasing to show art films, Bleecker Street Cinema had a short stint as a porno palace, then was renovated for retail use.
This page, from the 1965 Inside Guide to Greenwich Village, calls it “a film-lover’s paradise,” then lists other artsy theaters, most of which are long gone. Cinema Village still exists, but the Greenwich Theater is now an Equinox, and the Eighth Street Playhouse a retail outlet.