Vienna

The soaring Gothic cathedral at the dead centre of the city, its roof a dazzle of coloured tiles. Climb the south tower's 343 steps or take the lift to the north for the rooftop view, and step inside the cool, vast nave. The heart of Vienna.

The Habsburgs' summer palace — 1,400 rooms of imperial excess, and vast baroque gardens climbing to the Gloriette folly with a view back over the whole city. Do the state rooms, then lose an afternoon in the free grounds and the old zoo.

The Habsburgs' winter palace, a whole quarter of the city — the imperial apartments and the Sisi Museum, the Spanish Riding School's white horses, the treasury of crowns and jewels. Six centuries of empire, all in one vast complex.

Two baroque palaces and formal gardens, holding the world's greatest collection of Gustav Klimt — above all 'The Kiss', shimmering with gold. Worth it for that one room, and the garden view back to the old town is a bonus.

A UNESCO-listed institution — order a melange and a slice of Sachertorte or apfelstrudel, take the newspaper on its wooden holder, and stay as long as you like. Café Central, Sacher, Hawelka: pick a grand old one and do nothing beautifully.

One of the great opera houses of the world, and gloriously democratic — standing-room tickets go for a few euros on the night, so anyone can hear world-class opera under the chandeliers. Dress up, or just take the tour by day.

The grand boulevard that replaced the old city walls, ringed with monumental buildings — the Parliament, City Hall, the museums and the university, one after another. Ride tram 1 or 2 around it, or walk it; a lesson in imperial ambition.

One of the world's largest cultural complexes, in the old imperial stables — the Leopold (Schiele and Klimt), the modern-art MUMOK, and a set of courtyards where the whole city hangs out on painted benches with a drink. Culture and chill in one.

Vienna's big, buzzing market — a long run of stalls selling cheese, olives, spices and street food from around the world, with a flea market on Saturdays. Graze your way along, then grab a table for lunch. The city's tastiest wander.

The great public park across the canal, and the giant 1897 Ferris wheel that crowns it — a slow, romantic turn over the whole city, straight out of The Third Man. Around it, an old-fashioned funfair and miles of green to walk or cycle.

The most striking baroque church in the city, its great green dome flanked by two carved columns, reflected in a pool out front. A lift inside takes you up under the frescoed dome — an unusual close-up on a masterpiece.

A riot of a social-housing block by the artist Hundertwasser — wonky floors, mismatched windows, gold onion domes and trees growing out of the walls, a rejection of the straight line. Free to admire from outside; a joyful antidote to all the marble.

The white 'golden cabbage'-domed temple of the Vienna Secession, built by the artists who broke from tradition — inside, Klimt's shimmering Beethoven Frieze runs around a basement room. A jewel-box of Jugendstil, small and dazzling.

A pocket of cobbled Biedermeier streets behind the MuseumsQuartier — candlelit wine taverns, little bars and restaurants in old townhouses, and one of the loveliest Christmas markets in December. Vienna's most charming spot for an evening out.

Vienna is the only world capital with real vineyards inside its limits, and the heurigen are where the new wine is poured — rustic taverns in the wine villages of Grinzing and Nussdorf, with cold cuts and a garden. Take tram D or the 38; utterly local.