The Biblical city names of Sodom and Gomorrah have been used to describe any modern city that is sinful. New York City (nicknamed “Gotham”) has infrequently been called a “Gomorrah” or the “Modern Gomorrah.” Other American cities—especially Chicago—have also been called these names.
 
New York City was called a “modern Gomorrah” in 1854. “There are to-day, influences abroad, which, if unresisted by the pulpit and the printing-press, will turn New York and Brooklyn into Sodom and Gomorrah” was said by Brooklyn Tabernacle Rev. Thomas De Witt Talmage (1832-1902) in 1875.
 
   
Wikipedia: Sodom and Gomorrah
Sodom and Gomorrah (/ˈsɒd.əm/; /ɡə.ˈmɔr.ə/) were cities mentioned in the Book of Genesis and throughout the Hebrew Bible, the New Testament and Deuterocanonical sources, as well as the Qur’an. According to the Torah, the kingdoms of Sodom and Gomorrah were allied with the cities of Admah, Zeboim and Bela. These five cities, also known as the “cities of the plain”, were situated on the Jordan River plain in the southern region of the land of Canaan. The plain — which corresponds to the area just north of the modern day Dead Sea) — was compared to the garden of Eden[Gen.13:10] as being a land well-watered and green, suitable for grazing livestock. Whether or not they ever existed is disputed by archaeologists.
 
Divine judgment by Yahweh was then passed upon Sodom and Gomorrah along with two other neighboring cities that were completely consumed by fire and brimstone. Neighboring Zoar (Bela) was the only city to be spared during that day of judgment.[Deut.29:23][Gen.10:19] In Abrahamic traditions, Sodom and Gomorrah have become synonymous with impenitent sin, and their fall with a proverbial manifestation of God’s wrath.[Jude 1:7] Sodom and Gomorrah have been used as metaphors for vice and homosexuality viewed as a deviation.
 
Google Books
February 1854, Graham’s Magazine, “Among the Mountains” by Frank Forester, pg. 146, col. 2:
... though he was a nobody while showing himself the cleverest young lawyer and most brilliant magazinist of New York, until, a small legacy falling to him, he deserted the dollar-worshipers and their Babel, for a retreat among the lakes, where he led what the Wall-streeters called a useless life, with a few old friends, a good many old books, a little old wine, and an innocent, charitable and kindly heart—a thing which, if it exist at all, has neither value nor honor in the modern Gomorrah.
 
Google Books
Sports that Kill
By Thomas De Witt Talmage
Wakefield: William Nicholson and Sons
1875
Pg. 139:
There are to-day, influences abroad, which, if unresisted by the pulpit and the printing-press, will turn New York and Brooklyn into Sodom and Gomorrah, fit only for the storm of fire and brimstone that whelmed the cities of the plain.
 
Chronicling America
24 November 1895, San Francisco (CA) Call, “Notes on Thanksgiving,” pg. 24, col. 5:
If New York society can make church attendance the fashion, Chicago can no longer jeer at New York as a modern Gomorrah.
A. OAKEY HALL.
 
Google Books
24 January 1903, The Outlook, “Books of the Week,” pg. 224, col. 2:
Although the scene might be laid in any great city where the boulevards are indirect juxtaposition to the slums, New York seems to be the modern Gomorrah portrayed.
(The Reformer by Charles M. Sheldon.—ed.)
 
Chronicling America
9 November 1903, The Evening World (New York, NY), Home Magazine, pg. 10, col. 1:
THE CITY’S MORALS.
Magistrate Flammer’s tribute to the improved morality of the metropolis makes agreeable reading. New York is not the modern Gomorrah many persons who persist in preconceived notions think it.
     
Google Books
February 1905, Black Diamond Express Monthly, pg. 29, col. 2:

 
7 January 1916, Trenton (NJ) Evening Times, pg. 6, col. 4:
BRONSON-HOWARD, WRITERS, SEES
NEW YORK AS MODERN GOMORRAH
 
Google Books
April 1920, Current Opinion, pg. 523:
PHILADELPHIA CRITICIZES NEW YORK
NEW YORK SCOLDED FOR ITS MORAL AND OTHER SHORTCOMINGS
THE City of New York is in a bad way, if we can believe an editorial recently appearing in the Saturday Evening Post, The editorial, which is more than a page long and is titled “Gotham and Gomorrah,” charges the metropolis not with the sins which so sensational a title might seem to indicate but with various moral and other shortcomings such as instability, irresponsibility and hysteria.
(...)
(Caption of cartoon—ed.)
LEAVINGTHE MODERN GOMORRAH
Herbert Johnson’s caricature (in the Saturday Evening Post) of the modern Lot and his wife.
 
Unz.org
7 November 1925, The Literary Digest, pg. 32, col. 1:
IS NEW YORK A MODERN GOMORRAH?
 
Google Books
New York City Guide
By Federal Writers’ Project
New York, NY: Random House
1939
Pg. 147:
The district, known later as the Tenderloin, became the scene of such wickedness that one crusading minister, the Reverend T. DeWitt Talmage, denounced the city that tolerated it as “the modern Gomorrah.”
     
TimeOut New York
Tue Jan 18 2011
A history of NYC nicknames
Gotham, Fear City, the Capital of the World—-historian Michael Miscone explains synonyms for the Big Apple.
By Jenna Flannigan
The Modern Gomorrah In the 19th century, Manhattan was the devilish opposite to Brooklyn’s piety. In 1875 at the Brooklyn Tabernacle, Reverend T. De Witt Talmage was among the first to attack NYC with this epithet, for failing to stop organized crime.