Thirty-seven years ago, Luna Luna landed in Hamburg, Germany: the world’s first art amusement park by visionary artists like Jean-Michel Basquiat, Keith Haring, and David Hockney.

The perfect age to experience “Luna Luna,” the restored art carnival now on display at the Shed in New York, might be 2. To a toddler, the futuristic pavilions designed by Salvador Dalí, Roy ...