Forget What the Song Says. Tony Bennett’s Heart Never Left New York.

There were the famous New York places where he was celebrated, like the Metropolitan Museum of Art, where his 75th birthday party wasn’t referred to as a birthday party. (The Met didn’t allow such things.)

There were the canvases he painted in every Manhattanite’s backyard. He knew just where to set up his easel in Central Park from looking out a window in his apartment and watching the reds pop in the fall or the greens in the spring.

And there were the New York stages he appeared on, from the Paramount Theater when he was in his 20s to Carnegie Hall in his 30s to Radio City Music Hall in his 90s.

Tony Bennett may have become famous for “I Left My Heart in San Francisco,” but his own heart was unquestionably a New Yorker’s. He had that New York cool, decade after decade — the kid from Astoria, Queens, who made a go of it in Manhattan.

“He was Mr. New York,” said the philanthropist Iris Cantor, a friend of Mr. Bennett’s. “That’s who he was.”

The city shaped him, from a hard-knock childhood with only-in-New-York breaks: As a 9-year-old, he sang at the opening of the Triborough Bridge (now the Robert F. Kennedy Bridge). And his fortunes seemed to run in tandem with the city’s: In the 1950s and ’60s he, and it, were flying high. In the ’70s, his popularity sank, torpedoed by the rock revolution, and the city’s finances imploded.

Both managed comebacks, Bennett with breathtaking moments when he was 60. And 70. And 80. And 90.

“Often he would do an encore without a microphone,” said the bassist Chip Jackson, who played with Mr. Bennett for almost a year in the 1980s. “Art Tatum could sound like 10 piano players at once. John Coltrane could play chords on his saxophone. Tony Bennett could make Radio City feel like he was singing in your living room. He had a way of projecting so everyone heard every word in the back row. He was the only one who could do that.”

Hoboken, across the Hudson River in New Jersey, could have Frank Sinatra. New York had Tony Bennett, who once said he loved Astoria more “than any place I’ve ever lived.” It was there that he and his wife, Susan, founded the Frank Sinatra School of the Arts, a public high school named for that other guy, one he considered a friend.

Mr. Bennett became a familiar presence at the school over the years, checking in on his passion project.

“He didn’t feel like a celebrity,” said Michele Quiles, who graduated from the school in 2012 and, like Mr. Bennett, grew up in Astoria. She said she “got the impression that having students be exposed and have access to art” had been a strong motivation for him.

Perhaps, but he also brought in big names, organizing impromptu assemblies with surprise guests like Paul McCartney or Billy Joel. He took the stage himself with Lady Gaga in 2014, performing songs like “I Can’t Give You Anything but Love” and talking with students about music and creativity.

At other times, in other New York places, he was the surprise guest, as at a 2009 celebration for the newspaper reporter and columnist Jimmy Breslin. Some of New York’s best-known journalists lauded (or roasted) Mr. Breslin, who, one attendee recalled, sat on the stage like an uncomfortable king.

Finally, the writer Pete Hamill, the master of ceremonies, said there was one more guest. The curtain opened. There was Mr. Bennett. Suddenly the big names in journalism were fanboys and fangirls.

He lasted by working with younger performers as he aged and by maintaining his singularly New York sound. “He was not the least bit derivative,” said Bill Boggs, who was the host of a television talk show in New York in the ’70s and ’80s and who remembered Mr. Bennett’s appearances on the show — as well as a more personal moment.

Mr. Boggs had taken his mother — “a Tony Bennett fan from rags to riches” — to one of Mr. Bennett’s performances in Philadelphia 15 to 20 years ago. They went backstage. His mother and Mr. Bennett chatted. “No just ‘Hi, Tony,’ but a conversation,” Mr. Boggs said, describing how Mr. Bennett had reminisced with his mother about a Philadelphia nightclub where he had appeared when they were younger.

“Every time I saw Tony Bennett after that, it was ‘Bill, how is your mother? Please tell her hello,’” Mr. Boggs said. “I was at Le Cirque for a Saturday lunch. Tony Bennett was at an adjacent table. When he was leaving, he came by and asked about my mother. The people I was with said, ‘Wow, you know Tony Bennett.’ I said, ‘Apparently he liked my mother more than he liked me.’”

By then Mr. Bennett was so famous that he was called on to preside at the opening of Madame Tussaud’s Wax Museum on 42nd Street. He stood with his statue and said that as someone who had had gallery shows, he had found it tedious to be a model.

“It took two hours to pose,” he said, while acknowledging that it had been worth the trouble: “The statue is a shockingly accurate reproduction of me.”

That was followed by a perfectly timed pause, then: “But the statue can’t sing.”

As for the birthday party that wasn’t a birthday party, it happened in 2001. Mr. Bennett was well known at the Met. Over the years, the guards had let him in when the museum was supposed to be closed so he could set up his easel and paint.

But a birthday party? That was a problem, even though Ms. Cantor, who is a Met trustee, was working on the arrangements.

“They said only people who are members or trustees” could have birthday parties there, she recalled on Friday. “I said no. I said once a year a trustee could do something there. I said I’d like to use this one time for Tony.”

So she and Mr. Bennett’s son Danny Bennett arranged a birthday party without calling it that.

“‘Seventy-five years’ seemed to satisfy the board,” Danny Bennett said at the time, “so that’s what we put on the invitations.”

Dan Barry and Troy Closson contributed reporting, and Kirsten Noyes contributed research.