“Little Armenia” was the area in Manhattan along Lexington Avenue, from East 20th Street to East 40th Street (called Murray Hill). “Little Armenia” is cited in print since at least 1924; Armenians moved to other boroughs and to the suburbs and few parts of ‘Little Armenia” survived to the 1970s and 1980s.
   
Today, the area is frequently called “Little India” or “Curry Hill.”
     
 
Wikipedia: Murray Hill, Manhattan
Murray Hill is a neighborhood on the east side of midtown Manhattan in New York City.
 
20 January 1924, New York (NY) Times, “Street of Horse Dealers; One Place in New York Where the Smell of Harness and Saddlery Still Prevails Over That of Gasoline,” pg. SM7:
THERE’S a kick in the old horse yet. Henry Benson will tell you so. henry spends all his days in East Twenty-fourth Street, the Street of the Horse Dealers.
(...)
Italians are here, and Greeks and Poles, and a swarthy proud ragman from Little Armenia, around the corner; he is graduated today from a pushcart ot the second stage of his climb to opulence.
 
16 June 1935, New York (NY) Times, “See New York First” by Victor H. Bernstein, pg. XX1:
If the European is interested in what Americana he can pick up in New York City, the American is fascinated by the city’s Old World corners—the Jewish quarter, Little Italy, Little Syria, Little Armenia, Little Spain.
 
28 April 1984, New York (NY) Times, “‘15 Massacre Still Stirs Armenian-Americans” by Marvine Howe, pg. 25:
By the 1950’s, the area of Manhattan East of Lexington Avenue from 20th to 40th Street was known as Little Armenia.
 
Armenians worked in New York’s garment industry, and set up their own food stores, restaurants, newspapers (Pg. 26, col. 1—ed.) and dance groups. Today, with greater affluence, many Armenians live on Long Island. But there are a few reminders of the old Armenian neighborhood in Manhattan; the imposing gold-domed St. Vartan Cathedral at Second Avenue and 34th Street, the older and smaller St. Illuminator’s Cathedral on East 27th Street, the Tashjian grocery, founded over 100 years ago, and the popular Ararat and Balkan restaurants.
 
25 August 1985, New York (NY) Times, “Rising Rents Threatening ‘Little India’” by Marvine Howe, pg. 39:
The first food and spice store in what later became Little India—Kalustyan’s, on Lexington between 28th and 29th Streets—was Aremnian,—a reminder that the neighborhood was once called Little Armenia.
 
New York (NY) Times
Patriarch Seeks to Rally Armenians
By JOSEPH BERGER
Published: October 25, 1987
(...)
Armenians in the New York-New Jersey metropolitan area are, perhaps, 100,000 strong. But there is no longer a Little Armenia along the southern stretch of Lexington Avenue in Manhattan. Armenians are now scattered in Bayside and Sunnyside, Queens, and Tenafly, N.J.
   
Ephemeral New York
April 30, 2012
When Murray Hill was “Little Armenia”
Little Syria, Little Hungary, the Jewish Quarter: Manhattan really used to be a collection of tight ethnic enclaves.
 
From the 1930s through the 1960s, Lexington Avenue below 34th Street was Little Armenia, a mostly forgotten neighborhood of immigrant rug merchants, grocers, and other small business owners.
 
“On First, Second, Third, and Lexington Avenues, a small Armenian community was established,” writes Paul Sagsoorian in the Armenian cultural magazine Ararat.