In late November, she made a surprise appearance at Unicef’s Snowflake Ball, where she presented an award to the pop singer Katy Perry, a prominent supporter of her campaign and who sang at the Democratic National Convention last summer. Weeks later she was photographed greeting friends at her granddaughter’s dance performance in Manhattan. On Dec. 13, the rapper Fat Joe posted a selfie with Ms. Clinton on Instagram after he ran into her at dinner at Rao’s. (According to Page Six, Mrs. Clinton was dining with the Hollywood producer Harvey Weinstein and his wife, the fashion designer Georgina Chapman.) And that same week Mrs. Clinton supped with Ralph Lauren at the Polo Bar as other diners, including Christie Brinkley, orbited her table.
One of those in attendance was Laura Brown, the editor in chief of InStyle, who wrote on her Instagram account that Mrs. Clinton and Mr. Lauren ate hamburgers that night: “Big, juicy, fantastic burgers. And wine, and chocolate sundaes.” Ms. Brown said hello to Mrs. Clinton and hugged her twice, writing on Instagram, “‘I love you Hillary Clinton,’ I said.”
For some, the appreciation is more than political. Steve Tyrell performs at the Café Carlyle every Christmas, where he croons Frank Sinatra hits and old standards for a holiday crowd. In early December, he got word that Marc Mezvinsky, the husband of Chelsea Clinton, made a reservation for him and his wife. They were a no-show. A few days later, Mr. Tyrell said in an interview, Ms. Clinton made a reservation for four.
Mr. Tyrell knows the Clintons; they have exchanged letters about his music for years. Chelsea played the singer’s recording of the classic “The Way You Look Tonight” at her wedding, he said. So when Mrs. Clinton, her husband, her daughter and her son-in-law arrived for the 8:45 show on Dec. 17, they were seated at a prime table near the stage.
“It was the first time they’d been out to see music, and I was completely knocked out,” Mr. Tyrell said.
He sang Ira Gershwin’s “I Can’t Get Started” and told a story about how he changed the lyrics on his 1999 album “A New Standard” to reflect the Clinton presidency. He sang “The Way You Look Tonight” for Chelsea. And he dedicated the last song of his set, “That’s Life,” to Mrs. Clinton. When he got to the lyrics about picking oneself up after falling flat, Mr. Tyrell said the crowd of 100 or so leapt to their feet and cheered. Mrs. Clinton beamed and clapped her hands overhead.
“It was a very personal performance,” Mr. Tyrell said. “It gave everyone this feeling that they were seeing something special.” Whatever one’s politics, said Mr. Tyrell, Mrs. Clinton’s decades of public service should be recognized. “I think she should be appreciated,” he said, “not be told: ‘Lock her up. Lock her up.’”
Mrs. Clinton has, of course, emerged for more formal affairs. On Tuesday, she attended the opening of a new exhibition and museum space at the State Department where the Hillary Clinton Pavilion bears her name. (The ceiling is made of glass.) She and her husband are expected to attend Mr. Trump’s inauguration on Jan. 20. And on Feb. 16, Mrs. Clinton will speak at a ceremony at Grand Central Terminal to mark the issuing of a stamp honoring the fashion designer Oscar de la Renta, a close family friend.
Through a spokesman, Mrs. Clinton declined to comment on her outings around New York.
There have also been more private family moments that onlookers have found themselves unexpectedly witnessing. On Dec. 27, Mike Smith, a fund-raiser for Episcopal Relief & Development and a former reporter for The New York Times, was with his family and friends at Mohonk Mountain House in New Paltz, N.Y., when one of the women in his group told him that Chelsea Clinton was working out on a treadmill. Later, at about 6:30 p.m., Mrs. Clinton and the former president, along their daughter and their son-in-law, sat down to supper in a semiprivate alcove in the dining room.
During the evening, Mr. Smith said, “the awareness of their presence built; we decided to send them a bottle of wine.” (It was Chianti.) Chelsea Clinton and her husband left after they finished their meal. “Everyone was buzzing but being respectful, keeping their distance,” Mr. Smith said. “But once Bill and Hillary got up and moved to the hallway, people started standing and applauding and, at that point, they stopped, and started greeting people.”
One of the women in Mr. Smith’s group introduced herself to Mr. Clinton. “Hey Hillary!” Mr. Smith recalled the former president’s telling his wife. “Look! These are the people who bought us the wine!” Mrs. Clinton, Mr. Smith added, posed for photographs and “seemed to be very moved, taking the time to greet every person.”
The next morning he found Mrs. Clinton waiting for her family at the breakfast table, looking at her cellphone. He decided to snap a photograph. “She was doing what we were doing,” he said. “Just hanging out with her family.”
During intermission at “The Color Purple,” Ms. Erivo, who is British but who was also a supporter of the Clinton campaign, said Mrs. Clinton, Mr. Clinton and Ms. Clinton came to her dressing room to say hello. “I didn’t expect her to come backstage,” Ms. Erivo said. “I thanked her for coming. She thanked me for what I did for the campaign. Everyone is rallying around her. She is doing a wonderful job at being graceful.”
So much so, after the curtain call, the actress Patrice Covington thanked the audience for showing up and noted that there were several well-known people in attendance. “I’m not going to call all of them out — I know you already know them,” she said. She paused and waved in Mrs. Clinton’s direction.
The crowd burst into another round of applause.
An earlier version of this article misstated the date of a dinner where Mike Smith saw Hillary Clinton at the Mohonk Mountain House. It was on Dec. 27, not Dec. 26.
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