According to the always-reliable Cinema Treasures:
Located on an ever-busy stretch of Avenue A, in the heart of the East Village, this theater is easy to miss. Opened as the Avenue A Theatre in 1926, it was operated by RKO, followed by Loew's, and was closed in 1959.
Today, it's merely a receptacle for retail space on the former orchestra level of the remains of the original auditorium, which have been converted into a health-oriented grocery store called the East Village Farm. The theater's lobby was also converted into retail space, but has been empty for several years.
Like other theaters in this area, the theater's auditorium runs parallel to the street, with a narrow entrance on Avenue A. Much of the theatre's exterior has survived, including its emergency staircase. The decorations in the auditorium are thought to survive, above the false ceiling of the ground floor store.
One of the Cinema Treasures commenters got a peak inside at the mysterious upstairs...perhaps this is where the never-ending supply of sea salt chips are stored...
And here's what the Hollywood looked like circa 1949:
Photos via Cinema Treasures commenters.