“I grew up with my ‘uncle’ Frank and we came here for years,” said Ms. Martin, who also wanted to correct the record regarding a line in the Patsy’s cookbook. “They said that I was in my teens in the 1950s, but I was not.”

Mr. Danza posed for pictures near a buffet of rigatoni, meatballs and chicken contadina. “It used to be, it wouldn’t have been so unusual in New York City for a restaurant to be around this long,” he said. “But luckily the family own the building, so they’re not under that kind of rental pressure that most small businesses are.”

Of course, everyone wanted to hear stories about Ol’ Blue Eyes.

“One night, we’re upstairs with 15 of Sinatra’s friends,” the elder Mr. Scognamillo said. “Everybody had a few drinks, and Sammy Davis was feeling no pain. He decides he wants to tease Sinatra.”

So Davis taunted Sinatra with the chorus of “Anything You Can Do,” prompting escalating displays of one-upmanship, like spreading salt on the floor for a soft-shoe shuffle.

“Finally, Sammy gets ticked off,” Mr. Scognamillo said, setting up the oft-told punch line. “He walks over there, takes out his glass eyeball, puts it on the table and says: ‘Beat that!’”