Manhattan’s East Village had a large Hungarian population by 1900. “Goulasch Avenue, by the way, is the local title for the Hungarian part of East Houston Street,” wrote the New York (NY) Evening Post in 1896. “Goulash avenue, a name under which the lower part of Second avenue is known on account of the good goulashes to be had there” was cited in 1910. Goulash is a popular Hungarian stew.
 
“Goulash Alley/Avenue” moved in the 1900s to Yorkville, at Second Avenue and East 79th Street.
 
   
Wikipedia: Goulash
Goulash (Hungarian: gulyás) is a soup or stew of meat and vegetables, seasoned with paprika and other spices. Originating from the medieval Kingdom of Hungary, goulash is also a popular meal in Central Europe, Scandinavia and Southern Europe.
 
Wikipedia: Houston Street
Houston Street (/ˈhaʊstən/ how-stən) is a major east-west thoroughfare in downtown Manhattan, running crosstown across the full width of the island of Manhattan, from Franklin D. Roosevelt East River Drive (FDR Drive) and East River Park on the East River to Pier 40 and West Street on the Hudson River. It generally serves as the boundary between neighborhoods, with Alphabet City, the East Village, NoHo, Greenwich Village, and the West Village lying to the north of the street, and the Lower East Side, most of the Bowery, Nolita, and SoHo to the south. The numeric street-naming grid in Manhattan, created as part of the Commissioners’ Plan of 1811, begins immediately north of Houston Street with 1st Street at Avenue A, although the grid does not fully come into effect until 13th Street.
 
The street’s name is pronounced “how-stən”, unlike that of the city of Houston in Texas, which is pronounced “hyoo-stən”. This is because the street was named for William Houstoun, whereas the city was named for Sam Houston.
 
Old Fulton NY Post Cards
27 May 1896, The Evening Post (New York, NY), “An East-Side Character,” pg. 8, col. 5:
Goulasch Avenue, by the way, is the local title for the Hungarian part of East Houston Street.
(...)
That was the answer; that was the true and really sad story of the merry Jew of Goulasch Avenue.
 
Google Books
Children of Men
By Bruno Lessing
New York, NY: McClure, Phillips & Company
1903
Pg. 44:
This, however, was frowned Upon, for Goulash Avenue — as the Hungarians laughingly call Houston Street — loves to keep its secrets to itself.
   
Google Books
Langenscheidts Sachworterbucher:
Land und Leute in Amerika
By Carl Naubert and E. Fleugel
Berlin-Schöneberg: Langenscheidt
1909
Pg. 19:
Goulash Avenue P wird die 2. Avenue in New York genannt, da dort viele Österreicher und Ungarn wohnen. grand Klavier.
     
Old Fulton NY Post Cards
6 October 1910, Daily People (New York, NY), “Fun for the Millions,” pg. 2, col3. 3-4:
What on earth could the “alte Tante” mean by that, judging others by itself, the letter was a fabrication by some comrade who lives on Second avenue, nicknamed “Goulash avenue.”
(...)
Mr. G. appeared in person in Goulash avenue, a name under which the lower part of Second avenue is known on account of the good goulashes to be had there.
 
Google Books
June 1922, Hearst’s International, pg. 70:
All in a Night
This story of Goulash Avenue, which is another name for Houston Street in New York, shows that romance still lives and fairy tales may yet be written, when done by Bruno Lessing
 
Google Books
Manhattan Kaleidoscope
By Frank Weitenkampf
New York,NY:  Charles Scribner’s Sons
1947
Pg. 4:
One remembers an Irish truckman on Sixth Street, early in the present century, deploring with somewhat bibulous sentimentality the change in the Avenue: “Aw, it used to be called Lover’s Lane, and now it’s Goulash Avenue,” which referred, of course to the Hungarian element that had invaded the lower part of the thoroughfare.