Four days in Vienna: still dressed for an empire

Start where the city does. The cathedral sits in the middle of the pedestrian streets rather than on a square of its own, so you come round a corner and it is simply there, black with soot and patterned on the roof in glazed tiles. It is mostly Gothic, but the oldest parts are Romanesque: the Giant Gate at the west front and the two Towers of the Heathens beside it date from the thirteenth century. Building in the Gothic style stopped in 1511, when the fashion moved on and the north tower was left unfinished, which is why the two towers do not match.

The nave is free to enter and the interesting parts are not. If you take only one guided thing, take the one that reaches the red marble tomb of Emperor Frederick III and the carved altar from Wiener Neustadt, neither of which you can get near on your own.

Then go and sit down. A coffee house on the first afternoon is the fastest way to understand what kind of place this is, and Hawelka, five minutes from the cathedral, is the least polished of the famous ones: dim, cramped, brown, with pictures stacked up the walls. In the evening, the opera. Standing places go on sale on the day and the queue starts about two hours before the curtain, so eat first.

The Hofburg is not a palace so much as a district that grew for six centuries and never settled on a style. Most visitors queue for the imperial apartments and the Sisi rooms and leave without finding the treasury, which is the better half of the building by some distance. Twenty rooms of Habsburg regalia: crowns, robes, reliquaries, a cradle given to Napoleon's son, and the imperial insignia of the Holy Roman Empire, which is about as close as objects get to being the actual furniture of European history.

In the afternoon, cross to Maria-Theresien-Platz for the picture collection, which is administratively part of the same museum and physically ten minutes away. The Kunsthistorisches is one of the great galleries of the world and the building is half the reason to go: a marble staircase, a domed café in the middle of it, and ceilings painted by a young Klimt. The Bruegel room is the largest gathering of his paintings anywhere, and on a quiet weekday morning you can have most of it to yourself.

Finish with coffee at Central, in the courtyard of a nineteenth century palace with a vaulted ceiling and a pianist. It is the touristy one and it is still worth an hour; go for the room and the cake rather than for lunch.

Go out to Schönbrunn early, on the U4, and be at the gate when it opens. The Habsburg summer palace is the most visited building in the country and the yellow front of it is a kilometre of imperial confidence. Two tours are sold: the shorter one takes in twenty two rooms, including Franz Joseph's spartan bedroom and Elisabeth's apartments, and the longer one adds Maria Theresa's eighteenth century interiors, which are the more extraordinary of the two. No photographs, and no backpacks.

The gardens are free and much bigger than they look from the terrace. Walk up the slope to the colonnade at the top for the view back over the palace and the city behind it, which takes about twenty minutes and thins the crowds out completely. Kennedy and Khrushchev were both received here during their 1961 summit, and the palace has been on the UNESCO list since 1996.

Back on the U4 to Karlsplatz for the other Vienna, the one that came after the emperors and could not stand them. The Secession building went up in 1897 as a gallery for artists who had walked out of the official art establishment, and it is a white cube under a dome of gilded laurel leaves that the Viennese immediately nicknamed the golden cabbage. Klimt's Beethoven Frieze is in the basement. Across the square, a baroque church with two Roman columns bolted to the front of it, which is a stranger idea than it sounds and looks magnificent at dusk.

Keep the last morning for the Belvedere, which sits conveniently between the centre and the main station. Prince Eugene of Savoy, the general who spent most of his career beating the Ottomans, built it as a summer place outside the walls: two palaces facing each other across a formal garden that steps down the hill, with the whole of Vienna laid out behind them.

The Upper Belvedere holds the Austrian national collection, and the reason most people come is one small square painting of two figures on a cliff edge, covered in gold leaf. The Kiss is smaller than the posters suggest and there is always a crowd in front of it, so go at opening. The rest of the Klimt room is better than it gets credit for, and the treaty that ended the Allied occupation and made Austria independent again was signed in the marble hall upstairs in 1955, then shown to the crowd from the balcony.

Wien Hauptbahnhof is about fifteen minutes away on foot, downhill, or a couple of stops on the D tram, so there is no need to rush the morning or to go back into town for your bags.