Solomon R. Guggenheim Museum

Frank Lloyd Wright's spiral on Fifth Avenue opened in 1959, six months after his death, and it is still the most famous argument about whether a building should compete with the art. Take the elevator up and walk down the continuous ramp toward the glass dome; the rotunda is the show. It is honestly awkward for paintings. Before it opened, twenty-one artists signed a protest that the sloping ramp would throw their canvases askew, and the gentle tilt is still noticeable. Large, bold works and single-artist shows that use the spiral work best, so check what is on before you plan the visit around a specific exhibition.