The 19 essential things to do in Vienna

The Habsburgs' summer residence, Schönbrunn took its baroque shape from 1696, then Maria Theresa had it enlarged and redecorated in the 18th century. Franz Joseph was born and died here, and Elisabeth (Sisi) had her apartments here. The palace and its gardens have been a UNESCO World Heritage Site since 1996.

The Grand Tour covers the whole piano nobile in about 75 minutes with an audio guide: the private apartments of Franz Joseph and Elisabeth, state rooms such as the Great Gallery, and Maria Theresa's chambers. Outside, the park runs down to the Neptune Fountain, then climbs to the Gloriette, with a view over the palace and the city.

In the heart of the old town, the Stephansdom combines a Romanesque west front, with the Giant's Door and the Heathen Towers, and a Gothic nave. Its south tower, completed in the 15th century, rises to 136 m, and the glazed-tile roof forms the double-headed eagle and the coat of arms of Vienna.

Beneath the nave, the catacombs hold the urns containing the organs of members of the Habsburg family. The south tower is climbed on foot up to the watchman's room; the north tower, which has a lift, houses the Pummerin, Austria's largest bell.

The Hofburg was the seat of Habsburg power from the 13th century until 1918. Each era added its own wing, from the Gothic chapel to the early 20th-century Neue Burg, so the palace now forms a whole district between the Ring and Michaelerplatz. It still houses the offices of the Federal President.

The most popular visit combines the Imperial Apartments of Franz Joseph and Elisabeth, the Sisi Museum and the Imperial Silver Collection. The same complex holds the Imperial Treasury, the State Hall of the National Library and the Spanish Riding School.

The first major building on the Ring, the State Opera opened on 25 May 1869 with Mozart's Don Giovanni. Hit by bombing in March 1945, it was rebuilt and reopened in 1955; the neo-Renaissance facade and the grand staircase survived.

The house company performs a repertoire of operas and ballets that changes almost every night from September to June. To see the auditorium without attending a performance, guided tours run during the day, depending on the rehearsal schedule.

Prince Eugene of Savoy had the Belvedere built in the early 18th century by the architect Johann Lukas von Hildebrandt: the Lower Belvedere, his residence, then the Upper Belvedere, used for receptions. A terraced French-style garden links the two palaces.

The Upper Belvedere holds the largest collection of paintings by Gustav Klimt, including The Kiss, alongside works by Egon Schiele, Oskar Kokoschka and French painters such as Monet and Van Gogh. From the top of the garden, the view runs towards St. Stephen's Cathedral.

The two museums face each other across Maria-Theresien-Platz, in twin palaces opened in 1889 and 1891 to display the Habsburg collections. The Kunsthistorisches Museum holds the largest collection of paintings by Pieter Bruegel the Elder, including The Tower of Babel and The Hunters in the Snow, as well as works by Titian, Velázquez, Rembrandt and Vermeer, an Egyptian collection and the Kunstkammer, the emperors' cabinet of art.

Opposite, the Naturhistorisches Museum displays meteorites, minerals and dinosaur skeletons, and above all the Venus of Willendorf, a figurine about 30,000 years old.

Behind the Opera, the Albertina occupies the former palace of Archduke Albert of Saxe-Teschen, who assembled here in the late 18th century one of the world's most important collections of drawings and prints, from Dürer, with his Young Hare, to Michelangelo, Raphael and Rubens.

These fragile works are shown in rotation in temporary exhibitions. The permanent collection covers modern art from Monet to Picasso, and the same ticket opens the Habsburgs' neoclassical State Rooms. The bastion terrace looks out over the Opera.

A former imperial hunting ground, the Prater was opened to the public by Joseph II in 1766. It combines two worlds: the Wurstelprater, an amusement park with free entry, and the Grüner Prater, a riverside forest crossed by the Hauptallee, a chestnut-lined avenue more than 4 km long.

The Giant Ferris Wheel (Riesenrad), built in 1897, has become a symbol of the city; its wooden cabins rise to about 65 m, and The Third Man shot one of its best-known scenes here.

Housed in the oldest wing of the Hofburg, the Imperial Treasury keeps the insignia of two empires. For the Holy Roman Empire: the Imperial Crown, made around the second half of the 10th century, the Holy Lance and the coronation sword. For Austria: the crown of Rudolf II, which became the crown of the Austrian Empire in 1804, with the sceptre and orb.

It also holds the Burgundian treasure and the Order of the Golden Fleece, the cradle of the King of Rome, Napoleon's son, and, in the ecclesiastical section, reliquaries and liturgical vestments.

Viennese coffee house culture has been on Austria's UNESCO inventory of intangible cultural heritage since 2011. Café Central, opened in 1876 in Palais Ferstel under neo-Gothic vaults, is the best-known address: the writer Peter Altenberg, whose statue sits at a table near the entrance, used it as his office.

The ritual is the same in the city's grand cafés, from the Sperl to the Hawelka: you order a Melange (coffee with frothed milk) or an Einspänner (black coffee under whipped cream), served with a glass of water, and you can stay a long time with the newspapers provided.

The State Hall (Prunksaal) of the National Library is one of the largest baroque libraries in Europe. Commissioned by Emperor Charles VI, it was built from 1723 to 1726 to plans by Johann Bernhard Fischer von Erlach, completed by his son Joseph Emanuel.

Beneath a dome painted by Daniel Gran, nearly 200,000 old volumes fill the shelves, including the personal library of Prince Eugene of Savoy. The institution descends from the Habsburg book collections and has borne its current name since 1920.

The Naschmarkt, Vienna's largest market, stretches for about 1.5 km above the Wien river, which is vaulted over here, from Karlsplatz to Kettenbrückengasse. Stalls of fruit, spices, cheese and Austrian wine alternate with Turkish, Greek and Asian food stands; on Saturdays a flea market sets up at its far end.

It is also a good way into Viennese cooking, served in the surrounding restaurants and in the Beisl, the neighbourhood bistros: Wiener Schnitzel, Tafelspitz (boiled beef with horseradish and apple sauce), Kaiserschmarrn and apple strudel.

Opened in 1870, the Musikverein is the home of the Vienna Philharmonic and one of the world's most renowned halls for its acoustics. Its Golden Hall (Goldener Saal), with its caryatids and gilded ceiling, hosts the New Year's Concert every 1 January, broadcast around the world.

Beyond the Philharmonic's concerts, which sell out fast, the hall programmes visiting orchestras, recitals and Mozart-Strauss concerts aimed at visitors. Other major classical venues: the Konzerthaus, the State Opera and, for sacred music, churches in the centre such as the Peterskirche.

Beneath the Capuchin Church on Neuer Markt, the Imperial Crypt (Kaisergruft) has been the Habsburg burial place since 1633. Founded at the initiative of Empress Anna, wife of Emperor Matthias, it holds 145 members of the dynasty, including 12 emperors.

The route follows the chronological order, from the plain 17th-century coffins to the double rococo sarcophagus of Maria Theresa and her husband Francis I, and on to the vault where Franz Joseph, Elisabeth and their son Rudolf lie.

Mozart lived from 1784 to 1787 in this flat on Domgasse, behind the cathedral: it is the only one of his Vienna homes that survives. He composed The Marriage of Figaro here, among other works.

The museum spans three floors: the flat itself, then rooms on late 18th-century Vienna, the composer's patrons, Freemasonry and his music. The audio guide is included in the ticket.

Built from 1983 to 1985 with the architect Joseph Krawina, the Hundertwasser House is a City of Vienna social housing block on the corner of Kegelgasse and Löwengasse. Multicoloured facades, windows that are all different, uneven floors and trees planted on the terraces express Friedensreich Hundertwasser's idea that a building should live with nature.

The flats are lived in and cannot be visited; you admire the building from the street. Opposite, Hundertwasser Village, a former workshop converted in the same spirit, gathers shops and a café.

The Danube flows north-east of the centre; it is a regulated branch, the Donaukanal, that runs along the old town at Schwedenplatz. Its banks have become a place to go out: authorised street-art murals, beach bars in summer and cycle paths along the water.

The river itself is reached by the U1 metro line. Danube Island (Donauinsel), about 21 km long, was built between the 1970s and the 1980s to protect the city from floods; it is now a leisure area with beaches, cycle paths and, in June, the free Donauinselfest festival.

Opened in 1862 on the former glacis of the city walls, the Stadtpark was the first public park created by the City of Vienna. It covers about 65,000 m² on both sides of the Wien river, with lawns, a pond and shady paths.

People come for the gilded statue of Johann Strauss II playing the violin, unveiled in 1921, and for the monuments to Schubert, Bruckner and Lehár. On the edge of the park, the neo-Renaissance Kursalon hosts waltz concerts.

Fiakers, two-horse carriages driven by a coachman in a bowler hat, have been running in the old town since the late 17th century. They wait on Stephansplatz, on Michaelerplatz in front of the Hofburg, on Heldenplatz and on Albertinaplatz.

The short route loops around the old town; the long one also takes in the Ring, the Opera and Parliament. The coachman comments on the sights along the way, in German or English.