Four days in Gothenburg: Sweden's second city, and the one that talks to strangers

Haga was the first suburb outside the city walls, laid out in the 1640s for workers, and by the 1970s it was slums scheduled for demolition. Enough people objected that most of it survived, and what stands now is a run of nineteenth century houses built in a very particular local way: a ground floor of stone, because the fire regulations demanded it, and two floors of painted timber above. The street is called Haga Nygata and it is now cafés and small shops.

It is also where the city has an ongoing arms race about cinnamon buns. Several places sell a hagabulle the size of a dinner plate, and while it is unquestionably a tourist product, it is also genuinely good and one is enough for two people. Have the coffee with it; Swedes drink more coffee than almost anybody and fika is a fixed part of the day rather than a break from it.

Then climb the hill behind. Skansen Kronan is a squat seventeenth century fort with a crown on the roof, built to defend the city from the Danes, who never attacked it, so it has never fired a shot in anger. It has been a prison, a museum and now mostly a viewpoint, and the grass around it is where Gothenburg sits in the evening looking out over the rooftops.

Start on the water, because the canals are why the city is shaped the way it is. The Paddan boats leave from Kungsportsplatsen, run about fifty minutes, and take you along the moat, through the two remaining canals and out into the harbour. The famous part is a bridge with about twenty centimetres of clearance, where the whole boat has to duck; everybody is told to lie down and everybody does. It is undignified and it is the best introduction to the layout you will get.

The City Museum is two minutes from the landing, in the building the Swedish East India Company built for itself in the 1750s. That company made a fortune bringing tea, porcelain and silk back from Canton and its warehouse is now the story of the region, prehistory to the shipyards. It also holds the Äskekärr ship, the only Viking ship found in Sweden, which is a fragmentary thing but the real article.

In the afternoon walk along the quay to Maritiman, which describes itself as the world's largest floating ship museum and consists of nineteen vessels tied together with gangways between them. You go through a destroyer, a lightship, tugs, a monitor and, best of all, a submarine, where the engine room is the width of your shoulders and the crew slept between the torpedoes. Two hours, and not for the claustrophobic.

Slottsskogen is a hundred and thirty hectares of parkland ten minutes from the centre by tram, laid out in the 1870s in the English style, and it is free in every sense. There is an observatory, a children's farm, a natural history museum that costs nothing, and a small enclosure of Nordic animals where you can look at a moose from about ten metres, which is closer than anybody sensible wants to be to one in the wild. In late spring the azalea valley comes out and half the city walks through it.

Cross the road to the Botanical Garden, which is on a different scale again: a hundred and seventy five hectares running up the hillside into a nature reserve, founded in 1923, with a rock garden built into an old quarry, an arboretum, glasshouses of orchids and, oddly, one of the last surviving Easter Island toromiro trees, a species extinct in the wild. Entry to the garden is a token amount or nothing at all depending on the season.

In the evening, Liseberg. It is the largest amusement park in the Nordic countries and the most visited attraction in Sweden, it opened in 1923, and it is built up a wooded hillside with the rides threaded between pines. Balder, the wooden coaster, is regularly voted among the best in the world by people who take that seriously. Go after seven, when the light goes and the lanterns come on and the queues drop, and buy the wristband rather than individual rides.

The art museum stands at the top of Avenyn behind a bronze Poseidon that the city has been making jokes about since 1931. Inside is one of the best collections of Nordic art anywhere, and the room to find is the Fürstenberg gallery on the top floor, a reconstruction of a private collection assembled by a Gothenburg patron in the 1880s and 1890s, when Scandinavian painters were coming back from Paris and turning what they had learned onto their own light. Carl Larsson, Anders Zorn, Ernst Josephson, Edvard Munch, all of them in one high room.

Walk back down towards the station through the Garden Society, a nineteenth century pleasure garden inside the moat with a palm house of cast iron and glass and a rose garden of thousands of plants. It costs almost nothing, it is ten minutes from the platforms, and it is a much better way to spend the last hour than sitting in the concourse.

The station is at the far end of the garden.