
I knew those opera house postcards would take over my life. Trawling for more images, I ran into the Century Opera House, aka the Century Theatre, aka the New Theatre. And the internet being what it is, one link led to another led to a Wikipedia article led to Flickr led to various online archives and so on and so on, until the number of tabs open in my browser window became almost obscene.
Construction on the New Theatre started in 1906 It was the project of one Heinrich Conried, a director of the Metropolitan Opera House, who liked the idea of a New York equivalent of the Comédie Française. The theatre opened in late 1909, at Central Park West and 62nd Street. Its Wikipedia article has a wonderful selection of photos published in The New York Architect that year.
The exterior:

The auditorium:

The main foyer:

And particularly noteworthy, from an operatic point of view, this poster:

And sure enough, the Met's performance database lists a whole series of performances at the New Theatre. Its inaugural production was Massenet's Werther, evidently produced under pressure, judging by this note, which was included in the program:
Owing to unforeseen delay in having the lighting apparatus, other stage mechanism and needed facilities completed, and the consequent impossibility to secure for this first presentation adequate stage rehearsals, the opera Werther cannot be presented this evening in full accordance with the standards of this company. The Metropolitan Opera Company and The New Theatre management, however, believe they are meeting the wishes of their patrons in not postponing the performance, but respectfully request the indulgence of the audience for unavoidable shortcomings.
You don't see those sorts of notes these days, do you? Perhaps part of the problem was that the conductor, director and most of the cast were all making their débuts. Only the Charlotte was an established Met star: Miss Geraldine Farrar. A wealth of performances followed: The Barber of Seville, The Bartered Bride (with Emmy Destinn), Manon (with Frances Alda, just two months before she married the Met's director, Giulio Gatti-Cassazza) and a number of shortish works which were paired with ballets. Pavlova danced Act I of Coppélia there, on various double bills, including a Sonnambula with Elvira de Hidalgo, who would go on to teach Maria Callas, and a Cavalleria Rusticana with Olive Fremstad as Santuzza. 1909 also saw the theatre host the world première of Rachmaninov's Piano Concerto No. 3, played by the composer himself.
But the relationship with the Met was shortlived — there's nothing in the database beyond 1910. The theatre's poor acoustics and less-than-brilliant location, a mile away from the theatre district, did it no favours, and by 1911 the building was being leased to various other managers — Ziegfeld among them — who changed its name. It was the Century Theatre, then the Century Opera House, then the Century Theatre again. Musical performances continued: the Internet Broadway Database lists a variety of musicals and operettas right up until the late 20's. And they evidently persisted with meaty opera too: I did find this 1913 program for Cavalleria Rusticana and Hansel & Gretel.
The theatre gods, however, were not on the Century's side. It failed, and in 1930 the building was demolished. In its place rose a building which shares its name, and which is still a distinctive part of the Manhattan skyline, the Century Apartments:
