LUKE: Oh, what show?
LORELAI: Levittown, it’s a new musical.
The musical that Lorelai is going to see with Alex, Sookie, and Jackson is fictional. Levittown is a hamlet on Long Island, New York, built by Levitt & Sons as a planned community for returning World War II veterans between 1947 and 1951.
It was the first mass-produced suburb, and became a symbol of the American Dream, and of racial discrimination – the Levitts would only allow whites to buy in the suburb, and as late as the 1990s, only a tiny portion of the community were non-white. They built other Levittowns in Pennsylvania, New Jersey, and Puerto Rico.
Oddly enough, a real play called Levittown – a drama, not a musical – opened off-Broadway in 2009, to lukewarm response, although successful enough to be staged a few times since then.
In real life, there weren’t any new musicals debuting in New York in February 2003.