Five minutes’ walk east up the hill from Bellevue is a square formally dubbed Heimplatz but known to every Zürcher as “Pfauen” (Peacocks), after the peacock statue over the famous Schauspielhaus theatre. The adjacent café, now a Mövenpick, was for decades known as the Pfauen Café, and was James Joyce’s favourite watering hole – it still has a peacock as its inn sign.

Dominating the square is Zürich’s Kunsthaus, Switzerland’s best gallery (Tues–Thurs 10am–9pm, Fri–Sun 10am–5pm; Fr.6 for the permanent collection only, or Fr.8–14 to include temporary exhibits; free on Sundays). As well as an expansive permanent collection, the Kunsthaus hosts a continuous flow of top-flight temporary exhibitions, advertised widely around town. If you visit just one art museum in the country, this should be it. You can pick up a handheld audioguide to the collections for Fr.6.

The collection begins even before you get inside: beside the main door is Rodin’s vivid Gate of Hell, while sculptures by Moore, Maillol and others dot the grounds.Inside, the ground-floor galleries house whatever temporary exhibit is on; for the permanent collection (“Sammlung”), head left up the stairs next to the ticket booth and double back on yourself at the top to begin with the medieval Masters of the Carnation, the leading Swiss painters of around 1500. Dutch and Flemish painting is represented by Rubens, Rembrandt, Hals and others. A narrow corridor leads through to the massive Graphics Collection (80,000 works, of which only a tiny fraction can be exhibited), but to keep the thread head left into the Venetian room, for Canaletto and El Greco. To one side of the Venetians are more canvasas from the Italian and Dutch Baroque. Head back to the Venetians and turn right for a complex of rooms devoted mainly to Swiss artists of the nineteenth century, including many works from Anker, Böcklin, Segantini and Füssli, who lived and worked for many years in London.

Back at the head of the stairs, turning left brings you into the new wing, housing a stunning collection of twentieth-century art. A broad selection of pop, concrete and abstract expressionist art is headed by a number of Warhols, a Rothko and a gigantic wall-sized installation by Baselitz. Up the stairs here, past some geometric constructivist sculpture and a mezzanine with works by Bacon and Twombly, you’ll come to an area devoted to Alberto Giacometti, with the widest array of his sculpture in the world. This connects to the uppermost floor of the old wing which houses the best parts of the collection. A collection of French sculpture since Rodin is here dominated, unusually, by Matisse. Cubism, Fauvism and Dada are all represented, and works by Miró, Dalí and De Chirico head an impressive Surrealist overview. Picasso, Chagall, Klee and Kandinsky all have whole rooms to themselves, there are two of Monet’s most beautiful water-lily canvases, while Van Gogh, Gauguin, Cézanne and the largest Munch collection outside Scandinavia top an extraordinary journey. Last but not least is the rare chance to revel in the powerful, mystical landscapes of Alps and lakes by the Swiss painter Hodler.