US Census 1880: New York, New York City-Greater, New York (Manhattan), District 293, 1 32th St (that's really in the center, not too far from Madison Square Garden).
1880: Saloon Keeper
There is a registered death of a William Becker 14 Jan 1901 New York City. Not sure if it's the same William Becker.
There are also several William Beckers (same birth year) enlisted for the Civil War (New York D or E Company).
US Census 1870: New York, New York, New York Ward 20, District 19. Occupation: Keeps a Saloon. According to this census born abt 1821. His wife Julia born abt 1831. At the same address also stayed: John Dorson (58, Germany), stone cutter; Henry Wise (26, Switzerland), machinist, John Couts (30, Switzerland), machist; Jacob Morris (22, Germany) safe maker.
The name Becker is both German and English. Its origin may be (1) a place name: dweller at a brook; or (2) an occupational name: one who made bread, a baker. Source: E.C. Smith, New Dictionary of American Family Names, 1973.