“The Rialto” was the 14th Street theatre district. The theatre district has long since moved uptown, and “the Rialto” is no longer used. The term was extremely popular in the second half of the nineteenth century. “The Rialto” was later used for the uptown theatre districts, but it lost currency in the 1930s.
   
“Ragtime Rialto” was another name for the area of West 28th Street between Fifth and Sixth Avenues, also called “Tin Pan Alley.”
       
   
Wikipedia: Rialto
The Rialto is and has been for many centuries the financial and commercial centre of Venice. It is an area of the San Polo sestiere of Venice, Italy, also known for its markets and for the Rialto Bridge across the Grand Canal.
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The Rialto is also mentioned in works of literature, notably in Shakespeare’s The Merchant of Venice, where Shylock asks “What news on the Rialto?” at the opening of Act 1, Scene III, and Solanio in Act 3 Scene I poses the same question. In Sonnets from the Portuguese Sonnet 19, Elizabeth Barrett Browning writes that “The soul’s Rialto hath its merchandise…”.
 
Wikipedia: Union Square (Manhattan)
The Rialto
The Rialto, New York City’s first commercial theater district, was located in and around Union Square beginning in the 1870s. It was called the Rialto after the commercial district in Venice.  The theater district gradually re-located northward, into less expensive and undeveloped uptown neighborhoods, and eventually into the current Theater District.
 
Before the Civil War, theatres in New York City were primarily located along Broadway and the Bowery up to 14th Street, with those on Broadway appealing more to the middle and upper classes and the Bowery theatres attracting immigrant audiences, clerks and the working class. After the war, the development of the Ladies’ Mile shopping district along Fifth and Sixth Avenues above 14th Street had the effect of pulling the playhouses uptown, so that a “Rialto” theatrical strip came about on Broadway between 14th and 23rd Streets, between Union Square and Madison Square.
 
27 June 1886, Brooklyn (NY) Daily Eagle, pg. 6: 
He had a clear, dark, laughing eye and a dark mustache, that would have been better than a fortune to a Rialto stroller.
 
28 April 1889, New York (NY) Times, “How to See New-York City,” pg. 17:
On the south side of the square, between Broadway and Fourth-avenue, are the Morton House and the Union-Square Theatre. The sidewalk in front of these establishments is known as the “Rialto,” because it has been for years the favorite lounging place of actors when they gather for gossip.
   
Google Books
The City in Slang:
New York Life and Popular Speech
By Irving Lewis Allen
New York, NY: Oxford University Press
1993
Pg. 61:
Until the 1880s, the south side of Union Square on 14th Street was called The Rialto, after the name of the busy commercial district in Venice. In the 1860s, actors lounged around the base of the great equestrian statue of George Washington, and there they had what they and passersby called the slave market for those seeing employment through the theatrical offices in the area.
 
Among show people, 14th Street was “the street” in the sense of an informal network of news and gossip. Hence, the famous New York phrase “What’s new on the Rialto?”, an inquiry about what was going on in show biz and later by extension in any world of endeavor. The question echoes the line in The Merchant of Venice, “What news on the Rialto?”