"I Left My Heart In San Francisco" was written in 1953 by George Cory (music) and Douglass Cross (lyrics) in Brooklyn, NY, when they had moved to New York City but were nostalgic for San Francisco.

Tony Bennett's signature song (first recorded by him in 1962) is "I Left My Heart in San Francisco." The somewhat anti-New York lyrics are these, at the start of the song:

"The loveliness of Paris
Seems somehow sadly gay
The glory that was Rome
Is of another day
I've been terribly alone and forgotten in Manhattan
And I'm coming home to my city by the bay
I left my heart in San Francisco..."


Wikipedia: I Left My Heart in San Francisco
"I Left My Heart in San Francisco" is a popular song, written in the fall of 1953 in Brooklyn, New York, with music by George Cory and lyrics by Douglass Cross (1920–1975) and best known as the signature song of Tony Bennett.
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Background
The music was written by George Cory, with lyrics by Douglass Cross, about two amateur writers nostalgic for San Francisco after moving to New York.

Although the song was originally written for Claramae Turner, who often used it as an encore, she never got around to recording it. The song found its way to Tony Bennett through Ralph Sharon, Bennett's longtime accompanist and friends with the composers. Sharon brought the music along when he and Bennett were on tour and on their way to San Francisco's Fairmont Hotel.

Newspapers.com
12 January 1954, Sheboygan (WI) Press, "Glamorous Contralto Gives Fine Performance At North," pg. 6, col. 6:
She (Claramae Turner - ed.) did the "Habanera" from "Carmen," a role that has won her plaudits, doing half in French as she originally learned it, and half in Carmen Jones manner, a clever ditty, "The Green Dog," and then a premiere of a song, "I Left My Heart In San Francisco," written especially for her by Cross and Corry.

Newspapers.com
18 January 1954, San Francisco (CA) Examiner, "Baghdad-by-the-Bay" by Herb Caen, pg. 27, col. 1
Hownize: Claramae Turner, the Metropolitan Opera star, has added a song to her concert repertoire. It's "I Left My Heart in San Francisco," by Geo, Cory and Douglass Cross, and she sings it, mit schmaltz, as an encore. Bravo.

http://onlyinsf.sfvisitor.org/travel_media/press.asp?rid=102
SONG
Official: "San Francisco"
Official ballad: "I Left My Heart in San Francisco"

YouTube
#TonyBennett #ILeftMyHeartInSanFrancisco #MTVUnplugged
Tony Bennett - I Left My Heart in San Francisco (from MTV Unplugged)
Apr 15, 2014
Tony Bennett
Tony Bennett performing I Left My Heart in San Francisco from MTV Unplugged
Listen to Tony Bennett: https://tonybennett.lnk.to/listenYD