Frank Lloyd Wright's white spiral, which the artists of the day signed a petition against. Take the lift to the top and walk down the ramp.
A building the artists hated
Wright got the commission in 1943 and the building did not open until 1959, six months after he died and sixteen years after he started. In 1956, twenty-one artists including Willem de Kooning and Robert Motherwell signed a letter protesting that the curved walls and the sloping floor would make it impossible to show paintings properly.
They had a point. The walls of the rotunda lean back, the floor slopes at three per cent, and the bays are shallow. Curators have been arguing with the building ever since, and the museum eventually built a rectangular annexe alongside for the work the spiral cannot take.
It is also, from the inside, one of the most pleasurable rooms in New York. The ramp coils up six storeys around an open void under a glass dome, and there is no moment where you have to decide which way to go next. You just keep walking.
How to see it
Lift to the top, then walk down. The exhibitions are hung to be read in that direction and the descent is gentle.
The rotunda usually holds a single large temporary exhibition, and what is on will determine how long you stay. The permanent collection — Kandinsky in depth, plus Picasso, Klee, Chagall, Léger and the Thannhauser Collection of Impressionist and post-Impressionist work including Van Gogh, Cézanne and Degas — is in the tower galleries off the ramp, and those are conventional rectangular rooms.
Solomon Guggenheim’s original interest was what he called non-objective painting, which is why the Kandinsky holding is one of the deepest anywhere.
Time and money
Ninety minutes is plenty unless the temporary show is one you care about. It is the fastest of the big Fifth Avenue museums to do properly.
There is a pay-what-you-wish window on Saturday evenings, released online in advance and gone quickly. Otherwise general admission is a fixed rate, with under-12s free.
Outside
The exterior is worth a minute from the far side of Fifth Avenue, where you can see the whole cone. Wright wanted it clad in red marble and was talked out of it. The tan-painted concrete it ended up with is closer to what he originally sketched in 1943, when the drawings were in red crayon.
It sits on Museum Mile, the stretch of Fifth Avenue from 82nd to 105th that also holds the Met, the Neue Galerie, the Cooper Hewitt, the Jewish Museum and El Museo del Barrio. One evening in June the whole stretch closes to traffic and every museum on it opens free — Museum Mile Festival, and it is one of the better free evenings in the city calendar.
More Museums

The Metropolitan Museum of Art
Two million objects across five thousand years, in a building you cannot see in a day. Pick three departments and accept that you are missing the rest.

Museum of Modern Art
Starry Night, the melting clocks, Les Demoiselles d'Avignon and Warhol's soup cans, in six floors that can genuinely be done in three hours.

American Museum of Natural History
The blue whale, the dinosaurs and the dioramas, in a rambling complex of twenty-odd interconnected buildings on the west side of Central Park.
