This classic piece of advise is given to visitors to New York City. In the early years of this century, people were swindled. I'd like to add that it doesn't pay to rent, either.
The New York Times FYI section asked me about this in 2002, and the earliest I could find then was a Times story from February 15, 1920, when it was described as an old swindle.
16 June 1914, Lincoln (NE) Daily Star, pg. 6, col. 4:
A St. Louis man has bought part of a bridge across the Mississippi. We can't help wondering if this is the same westerner who used to buy the Brooklyn bridge every season.
11 September 1914, Newport (RI) Daily News, pg. 4?,col. 1:
The old adage about the high birth rate of "suckers" finds new proof inthe daily records of the Manhattan police. Wireless wiretappers, smooth gentlemen who sell the Brooklyn Bridge or sections of Central Park to guileless foreigners, even the purveyors of green goods and gold bricks, still find victims in spite of the frequency with which they have been exposed.
Here are two names:
8 July 1928, New York Times, pg. 21:
_CONFIDENCE MAN JAILED._
_McCloundy, Who Once Sold the_
_Brooklyn Bridge, Faces Life Term._
William McCloundy, 68 years old, of Asbury Park, N. J., whose chief failing was selling the Brooklyn Bridge, lots in City Hall Park and other property he did not own, was held without bail on a charge of second degree grand larceny by Judge Vaum in Kings County Court yesterday.
According to detectives who extradited McCloundy on Friday night, he sold the Brooklyn bridge in 1901, for which he was convicted of grand larceny and served two and a half years in Sing Sing.
18 December 1928, New York Times, pg. 33:
_FORGER GETS LIFE TERM._
_G. C. Parker, Confidence Man_
_Once "Sold" Brooklyn Bridge._
George C. Parker, 58 years old, said by the police to be an old-time confidence man, was sentenced to Sing Sing for life by Judge McLaughlin in the Kings County Court yesterday. (...)
His early exploits are said to have included the "sale" of the Brooklyn Bridge...