“Taxi” (1972); “Mr. Cab Driver” (1989)

Neither "Taxi" nor "Mr. Cab Driver" is a New York City song, but both are about taxi drivers (something New York is known for). Also, the singer-songwriters of both songs have connections to New York City.

Harry Chapin got his start in New York City and lived on Long Island. His song "Taxi" is from the album Heads and Tales (1972). "Frisco" (that would be San Francisco, but they hate it when you say that) is mentioned in the song, as is "Parkside Lane." However, there is nothing else that particularly makes this a San Francisco song. One wishes that Chapin had written "New York" and "Morningside Drive" instead.

"Taxi" is a story-song about a taxi driver and a former flame who enters his taxi.

"Mr. Cab Driver" by Lenny Kravitz was from his album Let Love Rule (1989). Kravitz was born in New York, but grew up in Los Angeles. In the song, "Mr. Cab Driver" refuses to pick up a black passenger. It's not stated what city this takes place in, but such incidents have certainly (unfortunately) happened in New York.

http://users.cis.net/sammy/taxi.htm
It was raining hard in 'Frisco,
I needed one more fare to make my night.
A lady up ahead waved to flag me down,
She got in at the light.
"Oh, where you going to, my lady blue?"
"It's a shame you ruined your gown in the rain."
She just looked out the window, and said,
"Sixteen, Parkside Lane."

...
http://www.oldielyrics.com/lyrics/lenny_kravitz/mr_cab_driver.html
Mr. Cab Driver won't you stop to let me in
Mr. Cab Driver don't like my kind of skin
Mr. Cab Driver you're never gonna win

http://en.wikipedia.org/wiki/Harry_Chapin
Harry Chapin (December 7, 1942 - July 16, 1981) was an American singer and songwriter. He originally intended to be a documentary film-maker, and directed Legendary Champions in 1968, which was nominated for a documentary Academy Award. In 1971, he decided to focus on music. With John Wallace, Tim Scott and Ron Palmer, Chapin started playing in various local nightclubs in New York City.

http://en.wikipedia.org/wiki/Lenny_Kravitz
Lenny Kravitz (born Leonard Albert Kravitz on May 26, 1964 in New York) is an American singer, songwriter, record producer, and guitarist whose retro-style amalgam of rock, pop, funk, and even techno is inspired by such music icons as Jimi Hendrix and John Lennon. Half African-American and half Caucasian, Kravitz is the son of Hollywood producer Sy Kravitz and Bahamian actress Roxie Roker, best known as a regular on The Jeffersons.

7 April 1972, New York Times, pg. 25:
Harry Chapin Shows His Style
In Program at the Bitter End
By DON HECKMAN

Singer-songwriter fix Harry Chapin came into the Bitter End Wednesday night preceded by a rising hit song called "Taxi" and a virtual cloud of public anonymity. After hearing his first set, with its range of moods and songs that reached far beyond the limits of "Taxi," I don't expect Chapin to remain anonymous for very long.

Actually, of course, as with all overnight show biz arrivals, Chapin has put in a long apprenticeship, much of it at the Bitter End with his two brothers, and is hardly unknown to New York folk aficionados.

17 July 1981, Washington Post, pg. C17:
Harry Chapin, "Taxi" Singer, Dies
NEW YORK, July 16 (AP) - Harry Chapin, singer and composer of such popular, wistful songs as "Taxi" and "Sequel," died today after his car was struck from behind by a tractor-trailer on the Long Island Expressway. He was 38.

2 October 1989, Los Angeles Daily News, pg. L23:
Upping the ante, Kravitz delivered a sleek interpretation of his anti-racism rocker, "Mr. Cab Driver."