1 High in the Alps For a wonderful panorama of Switzerland's largest city, take the S10 Uetlibergbahn from the main station to the top of the 871-metre foothill. Twice an hour a train departs from Platform Two for the 23-minute journey, winding through forests of thick pine. On a clear day, the Alps glisten in the distance and Lake Zurich shimmers in the foreground, and both are framed by the velvety patchwork of the countryside. A hill-top hotel and restaurant beckon, as do a trellis of well-marked paths to dozens of different beauty spots, although comfortable shoes, warm clothing and walking sticks are recommended. One of the best walks snakes to Felsenegg, two hours away. The path along the woody ridge eventually reaches a cable car and train for a quick return to Zurich. 2 Fraumunster To observe Marc Chagall's superb stained-glass windows in all their glory, be sure to be in this medieval church and Zurich landmark by sunrise. Painted in 1970, when the Russian-born French artist was 83, the five elongated, horizontal-glass panels, in stunning blues, greens and yellows, come alive in the morning light. Depicted are Jesus, Jacob and the road to Zion; an orange panel on the left celebrates the prophets while another blue window to the right affirms biblical law. Chagall also painted an often-overlooked, but equally impressive, circular panel in the transept, showing the creation of the world and an interpretation of evolution. Am Munsterhofplatz, tel:  1/211-4100. 3 Altstadt Developed during the early medieval period, Zurich's pedestrian-only old town straddles the River Limmat and consists of several distinct areas. On the left bank, cobble-covered Rennweg is famous for its leafy squares and 16th- and 17th-century rowhouses, including Stadtarchiv, which holds the city archives. This is also home to the Zurich James Joyce Foundation, one of the largest repositories of the Irish author's works: Joyce lived, died and was buried in Zurich, at the Fluntern Cemetery. Across the river, the Roman settlement of Lindenhof claims the city's highest point and its two universities: the Karl Moser-designed University of Zurich and the Polytechnikum. To reach this small - but steep - bluff, take the Polybahn: a funicular dating from 1889 and a restored icon of the city, at the end of the Bahnhof Bridge. Below the plateau is Niederdorf, the tradesmen's quarter. Its picturesque winding alleys remain home to carpenters, silversmiths, bookbinders and other artisans, but boutiques, lively restaurants and coffee houses are moving in. 4 Lake Zurich Central to the city's allure, Zurichsee, as it is locally known, stretches southeast to the foothills of the Alps. Several tour operators offer itineraries ranging from 55-minute trips along the Limmat River to all-day excursions to the lake's southeast. You can also enjoy the lake by taking a stroll along its leafy shores. Tonhalle is along its western coast. Opened in 1895 by composer Johannes Brahms, it is home to the city's distinguished orchestra. Along the eastern shore is Zurichhorn Park and Le Corbusier House, the Swiss architect's last, and arguably best, work. Built in the mid-60s, it was renovated last year and consists of two modular cubes with exposed beams, at the top of which rests an enormous grey steel parasol. The house is now a gallery dedicated to Le Corbusier's work. 5 Kunsthaus Zurich Switzerland's finest art gallery and leading art museum houses an impressive collection of mostly 19th- and 20th-century works, particularly those by Swiss-born artists such as Alberto Giacometti and Camille Graeser. Dutch and Flemish masters are represented by Rubens, Rembrandt and Hals, and a Venetian wing glories in the works of Canaletto and Titian. Warhol, Newman and Rothko are among the artists representing the New York School in an impressive new wing. Elsewhere are works by Matisse, Miro, Picasso, Chagall, Kandinsky, Van Gogh, Gauguin and Cezanne. Monet's Garden, one of 10 temporary exhibitions held annually, runs until February 27 and contains hundreds of works by the master French impressionist. Heimplatz 1, tel:  1/253-8484; www.kunsthaus.ch . 6 Fountains Zurich's most underrated feature is its collection of more than 1,100 spring-fed fountains. Dating from the 15th and 16th centuries, they were initially the gossip hubs of neighbourhoods. In styles ranging from medieval to modern, and fed by cold, crystal-clear alpine drinking water, they speckle nearly every square and alley. Among the most ornate is the Weinplatz; located in the former wine-trading square, it features a wrought-iron lace cupola and a statue of a grape picker. Other fountains of note include that in the Marktgasse, crowned by a solider standing atop a lavishly coloured column; and Swiss sculptor Richard Kissling's 1889 bronze statue of a local politician in the Bahnhofplatz, which rises majestically from an auburn-coloured granite base. 7 Park Hyatt Zurich Unlike the handful of recently unveiled contemporary hotels, the new Park Hyatt flaunts its modernity in bold, stylish steel and glass in the heart of the city. The airy lobby, on the other hand, is fashioned from bamboo and blond woods, bathed in natural light and illuminated by oversized, custom-made artwork. The hotel's 142 guest rooms continue the lobby's theme, with floor-to-ceiling bay windows and open waterfall showers in blackberry granite. The property's focal point, however, comes with its eateries and bars. Since its opening in September, Onyx has trumped many of Zurich's traditional nightspots, and Parkhuus, the hotel's main restaurant, lures gastronomes. Beethoven-Strasse 21, tel:  1/43 883 1234; www.zurich.park.hyatt.com . 8 Bahnhofstrasse Lined with the stores of world-renowned labels, famous jewellers, restaurants and confectioners, this is Switzerland's best and most elegant shopping boulevard. Begin at the city's train terminus, Hauptbahnhof, where a daily farmers' market sprawls from under the steel girders of an open-air hall. Continue your culinary excursion at the Globus department store, now almost a century old, which last May opened an upmarket, modern food court on three levels. There are dozens of strictly upper-echelon watch shops along this pedestrian-only avenue, in addition to chocolatiers such as Confiserie Sprungli, home of the Luxemburgeli, a decadent cream puff. Home-grown retailers such as Bally, located in retro-cool headquarters, are prominent, as are many of the more than 350 banks based in Zurich. 9 Zuri-West The most liveable city in the world - according to a survey by London-based Mercer Human Resource Consulting - recently became even more inhabitable. Zuri-West, the city's former industrial heart, which received a Berlin-style makeover, had a lot to do with it. From the Hauptbahnhof, take the No4 or 13 tram a dozen stops to Escher-Wyss Platz, then walk west along Hardstrasse and past a host of chic galleries, elegant restaurants, a hotel, theatre and a dozen hip nightspots. Developers have also turned vast parcels of old factory grounds into green spaces and sculpture parks. Abutting it all are cutting-edge lofts, elegant office parks and a university annexe. 10 Landesmuseum The history of Switzerland is chronicled in meticulous detail behind the imposing neo-Gothic facade of the 19th-century Swiss National Museum. Nearly every aspect of Swiss life is explored, but highlights include the prehistoric section, whose artefacts date from the fourth millennium BC, and the hall of arms. In addition to its myriad period costumes, furniture and an entire gallery dedicated to the art of clockmaking, the museum holds temporary exhibitions to spruce up its staid image. Gene research and human development are examined in the exhibition running until January 2. Museumstrasse 2, tel:  1/ 218-65-11; www.musee-suisse.com .