He’s been called many things—tall, rugged, hazel-eyed, handsome, hunky, the Sexiest Man Alive. But 43-year-old Australian superstar Hugh Jackman likes it best when he’s home in New York City, being referred to simply as husband, father and Broadway star. That’s why the endlessly charismatic family man is happiest right now, as he’s singing, dancing and flashing his infectious smile across the footlights during the 10-week run of Hugh Jackman, Back on Broadway.

“I recently found a video on YouTube from my first visit to New York City in 1996,” says Jackman. “I’m in Times Square, pointing to the marquees of all these big musicals, like Cats and Rent, and saying, ‘Someday, my name will be up there.’ It’s a bit embarrassing to look at the video now, but it reminds me that this show is truly the one thing I’ve always wanted to do.

Backed by an 18-piece orchestra and surrounded by beautiful showgirls, Jackman—who won Tony and Drama Desk awards for his portrayal of pop music icon Peter Allen in The Boy From Oz (2004)—is performing everything from Sinatra to Rodgers and Hammerstein, following sold-out engagements in San Francisco and Toronto. The show might not have happened at all, if not for problems plaguing the next sequel in the blockbuster X-Men film series, in which Jackman reprises his role as a mutant with retractable steel claws. “Last year, I went to see Sting in concert in Detroit,” he explains. “My film agent, who was sitting next to me, turned to me and said, ‘Hugh, it’s finally time for you to do your own show.’ The truth is, I was always being asked to sing at charity benefits, and I’d point out that I didn’t have a musical repertoire. When the shooting of my film The Wolverine got cancelled the first time, earlier this year, I decided to try a show for two weeks in San Francisco. It was a great experience, but I knew the show needed work. So, we recently did it again in Toronto, and I thought that might be it for a while. Then I got a call from someone in Broadway’s Shubert Organization offering me a theater in September. I said ‘yes,’ thinking he meant September 2012. Then the film was pushed back again, so here I am!

Indeed, Jackman is thrilled to be back on the Great White Way. “There is nothing like New York City audiences,” he declares. “They’re really ready for a great night out. Some other places I’ve played, I feel like it’s my job to win them over. But on Broadway, they’re ready for the show the minute they walk in. And they’re really intelligent,” he adds. “If you don’t give them a great show, they know it and they’ll let you know!”

Not only does Jackman appreciate his fans, some of whom have been known to wait for hours outside the stage door just to shake his hand, but he actually looks forward to meeting and talking to them. “First of all, I know the feeling of being a fan,” he confesses. “Back in 1996, during that first visit to New York, I waited outside the stage door to meet Al Pacino when he was performing in Hughie. He scribbled something on a poster, probably the letter ‘A,’ and I still have that poster in my house. I also know how loyal my fans are, and it’s not a lot of time out of my life to say ‘hi’ or sign a Playbill after a show.”

He has also been known to literally give a fan the shirt off his back for a good cause, specifically Broadway Cares/Equity Fights AIDS. During the 2009 run of A Steady Rain, he and co-star Daniel Craig auctioned off T-shirts and other items of clothing immediately after each performance, raising more than $1.3 million for the charity in just six weeks. “This time, maybe I’ll just sell my body, or maybe I’ll just call Daniel every night and have him come out on stage with me at 10:20,” he jokes.

Now, being on Broadway means he can spend quality time in his sprawling Greenwich Village triplex with his wife of 15 years, actress Deborra-Lee Furness, and their children, 11-year-old Max and 6-year-old Ava. “From the day we met in 1995, Deb told me she wanted to live in New York; she had gone to school here and felt like she had grown up here. And you know what they say, ‘Happy wife equals happy life,’” says Jackman. “It’s such a stimulating place to raise our kids. Every week we go to the American Museum of Natural History or the Metropolitan Museum of Art. We spend time in Battery Park and bike along the waterfront. And just walking my daughter to and from school ... There really is a sense of community here.”

After the final curtain falls on his Broadway show, Jackman doesn’t expect to be able to spend much time at home in 2012. First, he’s heading to London to film the movie version of the Broadway musical, Les Misérables. Then, he anticipates The Wolverine will finally begin shooting. Yet Gotham is always in his heart. “The last thing I’d ever want is to go back to the suburbs of Sydney. I feel so lucky to live in New York.”