“Big Sleazy” is a nickname for New Orleans, Louisiana, that is basically a negative version of a popular nickname, “Big Easy.” The nickname “Big Sleazy” was published in The Times-Picayune (New Orleans, LA) on February 24, 1985 and January 11, 1986.
 
The “Big Sleazy” nickname was used frequently in the Dave Robicheaux series of novels (published in the 1990s and 2000s) by American author James Lee Burke. The fictional Robicheaux character was once an officer for the New Orleans Police Department.
     
Other New Orleans nicknames include “America’s Most Interesting City,” “Baghdad-on-the-Bayou,” “Big Crescent,” “Big Easy,” “Big Greasy,” “Birthplace of Jazz,” “Chocolate City,” “Chopper City,” “City of a Million Dreams,” “City of Yes,” “City That Care Forgot,” “City That Forgot to Care,” “Convention City,” “Crawfish Town,” “Creole City,” “Crescent City,” “Erb City,” “Gateway of the Mississippi Valley,” “Gumbo City,” “Hollywood South,” “Jump City,” “Mardi Gras City,” “Metropolis of the South,” “N’Awlins,” “Necropolis of the South,” “Nerlins,” “No Orleans” (after Hurricane Katrina), “NOLA,” “Northernmost Banana Republic,” “Northernmost Caribbean City,” “Old Swampy,” “Paris of America,” “Queen City,” “Saint City,” “Silicon Bayou,” “Silicon Swamp” and “Sweet Lady Gumbo.”
       
     
Wikipedia: New Orleans
New Orleans (/njuː ˈɔːrli.ənz, -ˈɔːrˈliːnz, -ˈɔːrlənz/, or /ˈnɔːrlənz/; French: La Nouvelle-Orléans [la nuvɛlɔʁleɑ̃]) is a major United States port and the largest city and metropolitan area in the state of Louisiana.
 
The population of the city was 343,829 as of the 2010 U.S. Census. The New Orleans metropolitan area (New Orleans–Metairie–Kenner Metropolitan Statistical Area) had a population of 1,167,764 in 2010 and was the 46th largest in the United States.
       
24 February 1985, The Times-Picayune (New Orleans, LA), “No Sale” by Lance Hill, TV Focus, pg. 8, col. 3:
This *The Shopping Channel—ed.) has got to be the most depressing snake oil show to ramble through the Big Sleazy.
 
11 January 1986, The Times-Picayune (New Orleans, LA), “Picayunes,” pg. A-18, col. 4:
Many civic-minded New Orleanians are afraid that the governor’s plan to legalize casino gambling will mean the death of “Big Easy” and the birth of “Big Sleazy.”
 
25 January 1990, The Times-Picayune (New Orleans, LA), “Party! The world is your erster in the Big Easy” by Angus Lind, pg. A-1, col. 3:
It’s been called everything from Big Easy to Big Sleazy to the City That Care Forgot and the City That Forgot to Care.
 
30 January 1990, Daily Press (Newport News, VA), “New Orleans not really Big Sleazy” by Warner Hessler, pg. D1:
Bring it back. Bring the Super Bowl back to the Crescent City again. And again. And leave it here.
 
But, please, don’t invite back some of the guests who turned The Big Easy into The Big Sleazy last week.
         
Google Books
Sunset Limited
By James Lee Burke
New York, NY: Hyperion
1993
Pg. 198:
“The Big Sleazy’s not your turf anymore, Streak.”
   
Google Books
American Hard-boiled Crime Writers
By George Parker Anderson and Julie B. Anderson
Detroit, MI: Gale Group
2000
Pg. 20 (James Lee Burke):
Robicheaux often takes jaunts into larger cities, especially New Orleans, which he refers to as “the Big Sleazy.”
 
National Review
The Big Sleazy
By RICH LOWRY
November 2, 2004 6:25 PM
Politics in New Orleans, Louisiana.
 
The New Yorker
Books
June 12, 2006 Issue
The Big Sleazy
How Huey Long took Louisiana.
By Elizabeth Kolbert
   
Google Books
The Tin Roof Blowdown:
A Dave Robicheaux novel
By James Lee Burke
New York, NY: Simon & Schuster
2007
Pg. 83:
“I say screw all these cock-suckers. Nobody jacks the Big Sleazy when the Bobbsey Twins from Homicide are on the job.”
 
Urban Dictionary
big sleazy
n. one who is of the highest level of sleaziness.
when big sleazy left, new orleans changed its name from the big easy to just the fleur de lis symbol in protest.
#big sleaze#sleazy#sleazeball#sleaze#sleazebag
by tupd April 19, 2007
         
Twitter
Nathan Aronson
@gr8n8no
Replying to @theharryshearer
@theharryshearer you should know that #NOLA has just as many nicknames, MSY, City that Care Forgot, Big Easy, Big Sleazy, NOLA, Crescent….
9:31 PM - 10 Apr 2011
 
Twitter   
Shane Low
@slow_motion20
The big easy a.k.a the big sleazy lmao
6:50 PM - 29 Nov 2013
 
Twitter
Barefoot Appalachian Li’l Abner Barbie
@HRHPrinceFrank
Big Easy -> Big Sleazy -> Big Queazy
11:51 AM - 10 Jan 2016
 
Twitter
Three Hammers
@ThreeHammersOKC
count down to NOLA is on lets make the Big Easy the Big Sleazy #NOLA #NewOrleans #roadtrip #threehammers
5:10 PM - 28 Mar 2016
 
Twitter
Kelly Dessaint
@piltdownlad
Ugh. The Big Easy is becoming the Big Sleazy. And not in the good way.Kelly Dessaint added,
Larry-bob
@larrybobsf
New Orleans: This Airbnb displaced 5 people
“This is my former house on Josephine st. where me, my ex and our neighbors were forced out of in the spring…”
via https://www.instagram.com/p/Be0xLCvnnuj/?taken-by=ediblespectacle …
5:08 PM - 6 Feb 2018 from Oakland, CA