The New York Times did some build up for the event.
And gave it a rave afterwards.
The venue was Koster & Bial's Music Hall at Broadway and 34th St.
The theater had been New York's opera house and it would soon be torn down to make way for Macy's grand new department store.
The projector was created by Charles Francis Jenkins and Thomas Armat; they quarreled and Armat sold it to Edison who bought it on condition he could claim to have invented it himself.
I can't find a video showing the film shown on April 23, 1896, but that same year Edison did make this little view of Herald Square where the music hall was located.
This drawing shows an artist's rendering of the Vitascope projector in operation at Koster & Bial's.
A site called Who's Who of Victorian Cinema gives some details: "The Koster & Bial's Music Hall stood at Broadway and Thirty-fourth Street, New York, where Macy's store stands today. John Koster and Albert Bial first opened a concert hall on 23rd St on 5 May 1879. In 1893 they bought the Manhattan Opera House from Oscar Hammerstein Sr, and, suitably remodelled, it re-opened as Koster & Bial's Music Hall. It was here that the Edison Vitascope received its premiere, on 23 April 1896. The projectionist was the projector's co-inventor, Thomas Armat... The music hall continued to include film presentations among its variety programme, including Biograph shows, until its closure on 21 July 1901, when the site was sold to Macy's. -- Koster & Bial's Music Hall, New York
The New York show was not the first time a movie had been projected before an audience. A few months earlier, on December 28, 1895, the Lumière Brothers had shown a film at the Salon Indien du Grand Café in Paris.
The movie at Koster & Bial's included an Umbrella Dance performed by the Leigh Sisters. According to the Silent Era the film "premiered 23 April 1896 at Koster and Bial's Music Hall in New York, New York, used as part of the premiere presentation of Edison’s Vitascope motion picture projection system."
Who's Who of Victorian Cinema
Koster & Bial on the Library of Congress web site. Extract: "On April 23, 1896, the Vitascope movie projector made its debut at Koster & Bial's Music Hall in Herald Square, New York City. The vaudeville circuit was a fitting venue because it not only provided a ready audience but also a source for film subjects including Annabelle, the 'butterfly dancer' and the theatrical production of 'A Milk White Flag.' During the premiere, film was projected onto a screen set within an gilt frame to create literally a "moving picture" for an amazed audience. This is an example of Koster & Bial's stock poster that was designed to be overprinted with information about a specific attraction."
"When were films first projected in a New York theatre?" by Larry Wild, Assistant Professor of Theatre, Northern State University.
Koster and Bial's Music Hall on wikipedia