"A, B, C, and D" for "Assault, Battery, Crime and Death" was used in the 1980s, but doesn't apply to the gentrified neighborhoods of today.
Amelia liked to hang out in Alphabet City, a low-rent area sandwiched between the East Village, the East River, and the Lower East Side. One night, she took me to a tiny, cramped bar on Avenue B: hard faces and wild eyes inside, dark streets and crumbling buildings outside. The place had a sense of danger, which I liked. Over many shots of whiskey, Amelia told me Alphabet City was notorious and the avenue names "A, B, C, and D" stood for "Assault, Battery, Crime and Death." I liked that as well. But she said it too was changing, and soon all of Manhattan would be too gentrified and expensive for any one normal to live in.
27 April 1984, New York Times, pg. A27:
The neighborhood, known as Alphabet City because of its lettered avenues that run easterly from First Avenue to the river, has for years been occupied by a stubbornly persistent plague of drug dealers in narcotics whose flagrantly open drug dealing has destroyed the community life of the neighborhood.
5 May 1984, New York Times, pg. 17:
"Alphabet City," which opened yesterday at the Manhattan I and other theatres in and around the city, is one of those exercises in romantic film making that owe more to the history of cinema than to the reality of the milieu that is their subject.
Here is a film that draws its title from the Lower East Side Avenues - A, B and C - that are is setting, and takes as its subject the criminal activities of a young man named Johnny (Vincent Spano), who has been granted this fief by organized crime.