Dusseldorf

The riverside road was sunk into a tunnel in the 1990s and the surface turned into a walkway. With the old town on the east bank, sunset falls over the far shore behind Oberkassel, and by evening the stepped embankment is packed with people sitting.

The old moat survives as a canal, lined with trees on each bank. The east row is luxury shops; across the water the west row is mostly banks and offices. The pond at the north end holds the Triton fountain, and locals shorten the name to the Ko.

The telecom tower stands just over 240 metres, and the round lights set along its shaft work as a clock. From the top down they show hours, minutes and seconds in turn, each split into tens and units, so count them at night from across the river.

On an old harbour quay, three warped buildings by Frank Gehry went up in 1999. One is white render, the middle one stainless steel sheet, the last red brick. It sits just south of the Rheinturm, so the two make an easy walk together.

Under the glass roof of the former state parliament, Tomas Saraceno's steel net hangs 25 metres up, and visitors crawl across it. You book a time slot, non-slip shoes are required, and you climb up in an overall lent at the desk.

South of the city by the Rhine stands an 18th-century pleasure palace painted pink. From outside it looks like a low single-storey building, yet inside are four floors with more than 80 rooms. The large park behind charges no entry fee.

This church near the old-town riverbank has a spire with a visible twist at the tip. The usual explanation is a roof frame built from unseasoned timber, and repairs kept the twist. Inside, a Gothic sacrament house survives.

The walls and sloping roof are covered in hornbeam hedge, about 8 kilometres of it laid end to end. In autumn the leaves turn brown and dry but stay on through the winter. Stand on the plaza before the theatre next door and the whole roof slope is in view.

North of the city on the Rhine, the thick stone walls of a palace rebuilt by Emperor Barbarossa stand in ruin. Climb up on them to see the river below; entry costs nothing. The old village lanes sit right behind and fit into the same stroll.

The museum stands in the valley where a limestone quarry turned up ancient human bones in 1856, in Mettmann east of the city. The find site is marked a short walk down the stream from the museum. A Neanderthal model dressed in a suit is its best-known figure.

Flagship of the state art collection, its curved black granite wall fronting Grabbeplatz. A bulk purchase of Paul Klee works in 1960 seeded the holdings, and Klee still has his own rooms. K21 sits elsewhere in town, so check the address first.

Housed in the red-brick Ehrenhof complex near the Rhine, built for a 1926 exhibition. It spans old masters to contemporary work, with an unusually large glass collection. The Dusseldorf School landscape rooms tend to be quiet enough to linger in.

Nicolas de Pigage laid it out for Elector Carl Theodor; it ranks as Germany's first park opened to the public and a model for Munich's English Garden. It begins where the Konigsallee ends, so shoppers walk straight out to a pond-side bench.

About 5,000 square metres inside Nordpark, given to the citizens by the city's Japanese community. Stones, bridges and pruned pines ring the pond. Entry is free, and spring, when the azaleas flower, is the best time to come.

Dusseldorf's only permanent weekday market, in Carlstadt just south of the Altstadt. Cheese, soup and fish counters sit among vegetable and flower stalls, and office staff eat standing at lunch. It is shut on Sundays; aim for a weekday afternoon.

In neighbouring Neuss, collector Karl Heinrich Muller began scattering galleries over 25 hectares of meadow and riverside wetland in 1982. Grassy paths link eleven brick pavilions by sculptor Erwin Heerich. Allow half a day and wear comfortable shoes.