Noguchi was born in Los Angeles but lived in New York, off and on, for nearly 70 years, creating many of the sculptures, stage sets, and industrial designs that made him one of the most successful artists of the 20th century. But “Noguchi’s New York,” at the Noguchi Museum in Long Island City, dwells in failure. Curated with ample affection by Kate Wiener, it surveys the artist’s relationship with the city. But it also resurrects, via models, archival photographs, and correspondence, more than two dozen unrealized or destroyed public projects, and details the myriad ways Noguchi’s adopted city relegated his expansive, democratic vision to filing cabinets.