But two celebrities have really stood out - Sandy Duncan and Cathy Rigby. That's right: Two iconic Peter Pans have come to throw their support behind the latest one.
"It was one of the best things I've ever seen and I don't usually gush but I'm protective of the part because I love it so much," said Rigby, who saw it Oct. 14. Duncan caught it - for the second time - three days before. "I can't say enough about it," she said.
The inventive show, adapted by "Jersey Boys" co-writer Rick Elice from Dave Barry and Ridley Pearson's best-selling 2004 children's adventure book, tells the story of how an English orphan became Peter Pan.
It digs into a story that both Duncan and Rigby have thought a lot about. Duncan, 66, played Peter more than 550 times on Broadway starting in 1979 and then took her role out on tour. She estimates she's played the boy who won't grow up at least 1,000 times.
Rigby, 59, has never really left the role, playing it on Broadway in 1990, then taking it on tour from 1998-99, which led to another tour from 2004-05, and has been on the road since 2011. She just took it to Macau, where she learned to say "Do you believe in fairies?" in Chinese.
While "Peter and the Starcatcher" features 12 actors in 20 scenes playing 50 characters, the nights Duncan and Rigby came by were perhaps most stressful for Adam Chanler-Berat, who plays Peter.
"It felt like Peter was out there watching me do Peter," says Chanler-Berat. "Sometimes, to motivate yourself, you pretend like the person that you're playing is out there in the audience that night and in some ways it felt like that."
Although he's never seen either woman play the role - he admits he was a fan of the Mary Martin version and the animated Disney film growing up - he quickly learned about the other Peters.
"When you take on this sort of project, the legacy follows with you, and I was very aware of the famous women that have played the part before," says Chanler-Berat, whose other credits include "Next to Normal" and the recent off-Broadway revival of "Rent."
"I was really struck by the graciousness of the two of them," he added. "To someone who's been with the part for such a long time, it was nice and relieving to know that they felt like we're doing this story justice."
One thing that calmed Chanler-Berat was the fact that his show is a prequel, meaning he had artistic license. "It's like the ultimate trump card," he says, laughing. "It's like, `I was the prequel. I came before so I can escape any responsibility.'"
"Peter and the Starcatcher" uses simple props - a few lengths of rope for a ship's hull, a yellow kitchen glove becomes a tropical bird and spray bottles of water mimic crashing waves. One crowd-pleaser is the character of Black Stache, a pirate with a huge fake mustache who will later be known as Captain Hook.
Both women hope the Tony Award-nominated show will endure past its closing date of Jan. 20. Even if it doesn't, a national tour will be launched in 2013 starting in Denver.
"It's so inventive and so hysterical and just captures, I think, the magic. The heart of the story is there," said Rigby, who is scheduled to keep swinging around as Peter during her current tour until April.
While the cast may have been nervous to meet the actresses, Rigby had her own odd moment when she saw "Peter and the Starcatcher." As the last scene unwound, she fished in her purse for her lipstick and put it on her lips.
"Then I realized that I just bought a black eyeliner pencil. So, in the dark, I'm actually putting black eyeliner all over my lips," she said, laughing. "I'm thinking Black Stache has cursed me. I wiped it off with the inside of my sleeve and laughed at myself for being so silly."
In the end, Chanler-Berat says he was deeply touched by meeting the other Peters. All three are very different people but they have something special in common.
"It's funny, you've never met that person before but you know a great deal about that person," he says. "That's what it felt like. It felt like you all shared a secret that no one else has."