Three days in Malmo: a shipyard that turned itself into a beach

Stortorget was laid out in the 1530s by clearing a block of the medieval town, which at the time made it one of the largest squares in northern Europe. The town hall on the east side dates from 1546 behind a Dutch Renaissance front added three hundred years later, and the fine stepped gable house in the corner belonged to Jörgen Kock, a German immigrant who became mayor and made his fortune by the straightforward method of running the royal mint. In the middle is a bronze of Karl X Gustav, the Swedish king who took the town off the Danes, sitting on a horse and looking pleased about it.

Lilla Torg, immediately south west through an archway, is the opposite in every way: small, irregular, laid out in the 1590s as the market overflow, surrounded by half timbered merchant houses and now entirely given over to outdoor tables. It is where Malmö sits in the evening and it is unashamedly the tourist square, which does not stop it being a good one.

Keep walking west into Gamla Väster, the old western quarter, which is where the town's medieval street plan actually survives. Low painted houses, cobbles, art galleries and design shops, no cars to speak of, and almost nobody about. Twenty minutes of wandering here is the best hour of the first day.

Malmöhus is the oldest surviving Renaissance castle in Scandinavia, built by a Danish king in the 1530s on the site of an earlier fortress, and it has had a long and slightly undignified career. It was a royal residence, then a fortress, then for eighty years a prison, and it is now four museums at once: art, natural history, the city's own history, and an aquarium, all on one ticket, which makes for a genuinely odd hour and a half where you go from Nordic modernist painting to a tank of tropical fish without leaving the building. The moat and the earthworks around it are a park.

From the castle, walk west along the canal and the old fortification line into Kungsparken and out to the sea. It is about twenty minutes to Ribersborg, which is two kilometres of made beach with shallow water, grass behind it and the whole of Malmö on it the moment the temperature reaches twenty. Out on a pier at the far end is the Kallbadhus, a cold bath house from 1902 with separate men's and women's sections, wood fired saunas, no swimming costumes, and steps going down into the Öresund. It is open all year. In January people do it anyway.

Carry on north into Västra Hamnen, built on the Kockums shipyard site, where the Turning Torso stands: nine cubes of five storeys each, rotated ninety degrees from bottom to top, a hundred and ninety metres high and completed in 2005. It is flats, so there is nothing to go up for, but the promenade below it is where the city drinks in the evening with the bridge to Denmark on the horizon.

St Peter's, a couple of streets from the main square, is a fourteenth century brick Gothic hall church on the Lübeck pattern, which is what northern German merchants built wherever they traded, and it is the oldest building in the city. The interior was whitewashed at the Reformation, but the small merchants' chapel off the north aisle was walled up instead and so kept its medieval painting complete: vines, saints and grotesques over every surface. It is the single best thing in Malmö and it takes fifteen minutes.

Then walk ten minutes to the city library on the edge of Kungsparken, which is three buildings joined together and a lesson in how to do that. The original is a red brick castle from 1901 designed to look considerably older than it is. Attached to it is a glass cube by Henning Larsen from 1997, called the Calendar of Light, which is a single reading room the full height of the building with a glass wall onto the park and a floor of pale wood. You walk in for nothing, sit down, and watch the weather.

The station is ten minutes north and the Copenhagen trains leave every twenty minutes.