Kelsey Grammer met me for lunch at one of his favorite restaurants, Nobu Fifty Seven, the Japanese mecca in Midtown Manhattan. “Good to see you,” he said, shaking my hand. “Kelsey.”

This relaxed, instantly likable man has been among the most recognizable figures in America since his phenomenal two decades playing the endearingly know-all shrink Dr. Frasier Crane on Cheers and Frasier. (Even his voice—as Sideshow Bob, on The Simpsons—is celebrated.) He knows the Nobu menu well. “The food here makes me very happy,” he said, ordering first courses for us to share. “May I have a double order of the yellowtail jalapeño? No garlic,” he asked the waiter. “Fantastic! And then an order of scallop tiradito, and four pieces of sea-urchin sashimi. How about a rock-shrimp tempura? Great! That will do it. And a tuna-sashimi salad. I think we’re good. Thanks, man.”

“You’re welcome,” said the waiter.

Mr. Grammer was rehearsing Finding Neverland, the new Broadway musical about J. M. Barrie and four of the boys who inspired Peter Pan (opening April 15 at the Lunt-Fontanne Theatre). He doesn’t enjoy rehearsing as much as most, though. “I like audiences and performing and, you know … applause!” The show marks the debut of movie mogul Harvey Weinstein as a marquee theater producer, and Mr. Grammer plays the pivotal role of Charles Frohman, the American theater producer of the original 1904 Peter Pan. “You’re the Harvey Weinstein of the period,” I suggested.

“Exactly! I told Harvey that I’m playing him! Maybe a little more refined, I don’t know.” At which he laughed good-naturedly. “I think this thing could run forever!” he said, admitting he’s an optimist by nature. “It has a great story, and it’s very uplifting and emotional. I defy anyone to have a dry eye at the end of the first and second acts.”

Mr. Grammer was about to turn 60. “It feels better than 40 did!” I mentioned that he used to be every tabloid’s dream with all the public dramas of his three former marriages and various scandals following him everywhere like prior convictions. “You know, there is a tide in the affairs of men,” he replied, quoting Brutus’s homily to eternal hope from Julius Caesar. He laughed again (and it’s catching). “I’ve learned to soldier on.”

And the tide has turned for the better. Four years ago, he married a British woman, Kayte Walsh, who’s in her mid-30s, and they live happily with their two children—he has six children in all—in Holmby Hills, L.A., and in New York City. “This lovely young woman lit up my world and changed my heart, which was a bit calloused and hardened against a lot of things. And we are good, and I feel young and alive.”

He certainly looked happy enough—and happier still with each delicious course. “Mmmm. You must try this!” Yet, at the height of Kelsey Grammer’s success, alcohol and cocaine addiction took him notoriously to the edge of self-destruction. “I’ll speak to the straight of it,” he offered, and his transparency was stunning. “That was the time when I could not forgive myself for my sister’s death.”

There are unimaginable family tragedies in this man’s life, which has been both blessed and cursed. When he was 13 years old, his estranged father was murdered—shot by a psychopath. His two half-brothers died in a scuba-diving accident. The sister he was referring to was 18-year-old Karen, who was abducted, raped, and murdered in Colorado by spree killer Freddie Glenn in 1975. There were two accomplices. Kelsey identified his sister’s body and then informed his stricken mother.