Tony Danza is making up for lost time.“One of the things I most regret about my life is that I didn’t take advantage of my youth,” said Mr. Danza, 75. “I had a great time, but nobody handed me an instrument and said, ‘Try this.’”Now he is learning how to speak Spanish, play the piano and a cornet.Mr. Danza, best known for his leading roles in the television series “Who’s the Boss?” and “Taxi,” has been entertainment’s jack-of-all-trades for decades. Yet he’s still striving to be the best singer, dancer and actor he can be.“What I am is a guy with finite time who wants to get in as much as he can while he can,” he said.Mr. Danza spent a Friday with The New York Times as he got ready for two performances, including a one-man show at Café Carlyle.10:13 a.m.The plan was to chat with Mr. Danza as he worked out in his Upper West Side bedroom. But he had exercised and meditated upside down on his inversion table earlier. On his way to change clothes, he picked up his boxing reflex ball. “I love to hit this thing,” said Mr. Danza, a former professional boxer. “For six and a half minutes, I’m just worried about hitting this ball.”10:43 a.m.Mr. Danza bought his 1954 Conn cornet at a pawnshop on Hollywood Boulevard in the early 1990s. He struggled to hit the note he was looking for. “I’m teaching myself how to play,” he said. “I bought a book.”1 p.m.Mr. Danza was down to one of his last performances in the three-man drama “Broken Snow” at Theatre 71. He grabbed a ukulele and started singing “Since I Fell for You” backstage. “Love brings such misery and pain / I guess I’ll never be the same / Since I fell for you,” he crooned. A stagehand said: “He serenades us every day. It’s such a treat.”3:39 p.m.In the drama, which also stars Tom Cavanagh and Michael Longfellow, Mr. Danza is a bad guy. He said he enjoys playing villains, and his character has reasons for being an awful person. “That’s what the play is about,” Mr. Danza said. “Finding out his reason.”3:58 p.m.Mr. Danza, a New York native, purchased his apartment on the Upper West Side in 2005. He has appeared on Broadway in “The Iceman Cometh” and “The Producers.” He would like to go back. “I want to be on the stage,” Mr. Danza said. “I have to choose wisely because how much time do I have left to do it? I don’t think that much.”4:40 p.m.Mr. Danza took the subway downtown to visit the headquarters of the Stars of Tomorrow Project, a nonprofit he co-founded that teaches young people from low-income communities in New York City how to act. “You get them with the acting, but you also teach them about life,” he said.5:16 p.m.Mr. Danza was giddy talking about Daniel Bravo Hernández, who trained at his nonprofit and was cast as Romeo in the upcoming Free Shakespeare in the Park production of “Romeo & Juliet” at the Delacorte Theater in Central Park. “He’s an incredible Shakespearean actor,” Mr. Danza said. “It’s unbelievable.”7:39 p.m.In a suite at the Carlyle, Mr. Danza put on his tuxedo for a four-day, sold-out Café Carlyle residency performing “Sinatra & Stories.” During the 80-minute show, he recounts his interactions with Frank Sinatra, who did a guest spot on “Who’s the Boss?” He also tap dances and sings 20 Sinatra classics. “I’m worried about my voice,” he said. “We will see what happens.”Over the summer, Mr. Danza will promote the fifth season of the Starz series “Power Book III: Raising Kanan.” In the fall, he will be back at the Carlyle with his new show, tentatively titled “More Standards & Stories.” His one-man show “Standards & Stories” debuted at the 90-seat nightclub in 2015. “It’s a gift to perform here,” he said.8:27 p.m.In the elevator to the lobby, Mr. Danza said his morning workout “felt like a long time ago.” But he said he did not consider himself to be a workaholic. “I’d love a day off, but I don’t know. This is fun. The play today was so much fun.”8:30 p.m.Mr. Danza performs with a four-piece band, including Dave Shoup, the group’s go-to comedian, on guitar. While Mr. Danza practiced his tap dancing in the lobby, Mr. Shoup told a joke involving New Jersey, a porta-potty, and “an angel getting its wings.”9:02 p.m.“The only thing I worry about is execution,” Mr. Danza said before taking the stage. Minutes later he crooned, “Come fly with me / Let’s fly, let’s fly away / If you can use some exotic booze / there’s a bar in far Bombay.”Produced by Gabriel Gianordoli, Shauntel Lowe, Elijah Walker and Eden Weingart.