Four days in Strasbourg: French and German by turns, and the food never changed sides

The cathedral does not reveal itself from a distance, it appears. The lanes bring you out at its feet with no warning and no square worth the name, and 142 metres of pink Vosges sandstone go up in front of you covered in carving. It was begun in 1176, finished in 1439, and from the seventeenth century until 1874 it was the tallest building in the world. Go inside for the rose window and the glass, which is largely medieval.

The astronomical clock is the other reason people queue. It is a sixteenth century case rebuilt in the 1840s, and the part everybody waits for, the apostles filing past a crowing cock while death strikes the hour, happens once a day early in the afternoon and needs a separate ticket bought that morning.

Across the square, the Musée de l'Œuvre Notre-Dame holds what the weather has driven indoors: the original statues off the west front, the workshop's medieval drawings on parchment, and a stained glass head from the eleventh century. Then eat under the carved timbers of the Maison Kammerzell, which has been an inn for most of its life and put those upper floors on in 1589.

The Palais Rohan was built in the 1730s for a prince-bishop of the Rohan family, on the riverbank behind the cathedral, and it is deliberately, aggressively French: after 1681 Paris wanted the new subjects to see what the crown looked like. It now holds three museums under one roof, and the honest advice is to pick one. The Fine Arts rooms are the strongest, with Botticelli, Memling, El Greco and a Courbet or two.

Walk west after lunch into Petite France, which was the quarter of the tanners, millers and fishmongers because the river split into channels here and gave them water. The half timbered houses have the open lofts under the roofs where hides were dried, the channels still run under the buildings, and the locks in the middle of it still work, so a barge going through is likely.

At the far end stand the Ponts Couverts, three bridges guarded by four square towers left from the old city wall, and behind them the Barrage Vauban, a weir Louis XIV's engineer threw across the river so the city could flood the plain in front of an attacker. Climb onto its roof terrace at dusk. That view, towers in front and cathedral behind, is the postcard, and it is free.

Strasbourg was given the Council of Europe in 1949 because putting the new institutions on the border that had caused the wars was the whole point, and the rest followed. The buildings sit together north east of the centre, twenty minutes by tram: the Parliament with its unfinished-looking tower, Henry Bernard's Council of Europe of 1977, and Richard Rogers' Court of Human Rights of 1995, which is the best of the three and looks like a ship's engine room in glass.

The Parliament is the one you can get into. It has a visitor centre that is free and open most days, and when a plenary session is running, which is four days a month, you can sit in the public gallery of the chamber and watch it happen in twenty four languages. Bring a passport. Sessions are listed months ahead, so it is worth a look before you fix the dates.

The Parc de l'Orangerie is across the road and is where to spend what is left of the day: a formal park with a lake, a bandstand, a small free zoo and an enclosure of white storks, around an orangery pavilion given to the Empress Joséphine. The stork is the emblem of Alsace and had almost gone from the region by the 1970s; the birds nesting on the roofs around here are the result of putting them back.

Finish with the Musée Alsacien, which is three old houses knocked together and connected by wooden galleries around a courtyard, and which is about how people here actually lived: painted furniture, farm tools, cradles, wine presses, and rooms for Christian, Jewish and older-than-either rituals side by side. It is the museum that explains the countryside you can see from the train.

Then walk north over the water into the Neustadt, the new town the Germans laid out after 1871 to make Strasbourg look like an imperial capital. It is enormous, straight, and built in a sandstone that nobody would mistake for French: the Place de la République is a ring of vast public buildings around a garden, with the old imperial palace on one side. It was added to the World Heritage listing alongside the medieval island, which surprised people who had spent a century calling it an eyesore.

The station is fifteen minutes west from there, and the market halls and bakeries on the way are the place to buy a kougelhopf mould you will use once.