Little Odessa (a term from the 1970s) is Brighton Beach, Brooklyn.
Wikipedia: East Village, Manhattan
East Village is a neighborhood in the New York City borough of Manhattan. Its boundary to the north is Gramercy Park and Stuyvesant Town, to the south by the Lower East Side, and to the east by the East River. Generally, although definitions vary on the neighborhood's exact street boundaries, the East Village is considered to be the area east of Broadway to the East River, between 14th Street and Houston Street.
Later waves of immigration also brought many Poles and, especially, Ukrainians to the area, creating an Ukrainian enclave in the city. Since the 1890s there has been a large concentration roughly from 10th Street to 5th Street, between 3rd Avenue and Avenue A. The post-World War II diaspora, consisting primarily of Western Ukrainian intelligentsia, also settled down in the area. Several churches, including St. George's Catholic Church; Ukrainian restaurants and butcher shops; The Ukrainian Museum; the Shevchenko Scientific Society; and the Ukrainian Cultural Center are evidence of the impact of this culture on the area.
Wikipedia: Brighton Beach
Brighton Beach is a community on Coney Island in the borough of Brooklyn in New York City. As of 2000 it has a population of 75,692 with a total of 31,228 households.
Brighton Beach was dubbed "Little Odessa" by the local populace long ago, due to many of its residents having come from Odessa, a city of Ukraine. In 2006, Alec Brook-Krasny was elected for the 46th District of the New York State Assembly, the first elected Soviet-born Jewish politician from Brighton Beach.
7 November 1955, New York (NY) Times, pg. 22:
THE egg jewelers of Little Ukraine, just east of the Bowery around Cooper Square, will show their gemmed eggs all this week at the Women's International Exposition in the armory at Park Avenue and Thirty-fourth Street.
19 May 1978, New York (NY) Times, pg. C18:
Bit of Ukraine on 7 St.
There are dozens of Ukrainian shops and cultural and fraternal organizations in "little Ukraine" and many of them will be open during the weekend.
18 May 1979, New York (NY) Times, pg. C25:
Ukrainuan-Americans will share their heritage in the section of the Lower East Side known as Little Ukraine. THeir festival takes place on East Seventh Street, between Second and Third Avenues.
31 December 1978, New York (NY) Times, pg. R1:
Attracted to the area by the beach, the smell of its salt wind and a breezy boardwalk to stroll along, most of Brighton's new immigrants are from Odessa--so many, in fact, that people are calling the area "Little Odessa by the Sea."
21 August 1979, New York (NY) Times, pg. B1:
Brooklyn contains at least hald the city's Soviet Jewish immigrants. Brighton Beach has been known for years as Little Odessa because a third or more of its residents come from there.