Cologne

Work began in 1248, halted for close to three centuries, and ended in 1880. Bombing flattened everything around while this stayed up. Shell marks and patches of other stone are still on the walls. The south tower is 533 steps with little room to stand aside.

Trains cross the middle without a pause while people walk the strips on either side. The locks on the railings weigh several tonnes; the office that owns the bridge has done the sums and leaves them there.

It stands on a spit in the Rhine, built like a ship, so water fills the windows. At the chocolate fountain a member of staff dips a wafer and hands it over. A greenhouse inside grows cocoa, whose pods hang straight off the trunk.

The roof is folded into zigzags, so from beside the cathedral it reads as a run of waves. Pop art and the Russian avant-garde share the building, and the Picasso holding is unusually deep.

A gondola line crosses the Rhine between the zoo bank and the Rheinpark. Four people ride one car, and it sways for a moment over open water. It opens in spring and folds up by October, so nothing runs in winter.

The tower carries 124 carved figures, every one of them tied to Cologne. Over the arch below, a face sticks its tongue out on the hour. It was put there to mock the old council, and its name means the jaw of the square.

The streets take their names from Belgian towns, so Brussels square runs beside Antwerp street. On summer evenings people sit drinking on the church steps there, and the noise has kept residents arguing for years.

It falls on the Monday before Ash Wednesday, so the date moves each year. Sweets are thrown from the floats by the sackful and caught in upturned umbrellas. Most trams and shops in the centre stop for the day.

Three buildings bent like harbour cranes lean out over the river on the site of the old docks. The upper floors project so far that from the promenade below they hang over your head.

Perfume has come out of this house since 1709, and the city lent its name to it. The only way in is with a guided round; nobody wanders it alone. At the end you lift a glass bell and smell the first blend.

The archdiocese's art museum, built by Peter Zumthor in 2007 over the ruins of the war-shattered St Kolumba church. Gaps in its grey brick walls let light filter over the ruins. No labels hang beside the works; instead visitors get a small booklet at the door.

One of Cologne's twelve Romanesque churches, its square tower with four corner turrets rising over the riverside old town. The east end bulges out in a rounded trefoil. Below ground, the remains of a Roman warehouse can be seen.

The Gestapo's building from 1935 until the war ended, now the city's Nazi documentation centre. The name comes from its owner's initials. On the basement cell walls, over a thousand inscriptions that prisoners scratched in pencil and fingernail survive.

The prince-elector's Augustusburg Palace and Falkenlust hunting lodge at Bruhl, between Cologne and Bonn, share World Heritage status. Balthasar Neumann's staircase is the showpiece. Bruhl station faces the palace gardens; step off the train and cross over.

A house on Bonngasse in Bonn, a short train ride from Cologne, where Beethoven was born in an attic room in 1770. The brass ear trumpets he used as his hearing failed sit in a glass case. A small hall next door holds concerts on instruments of his era.