Four days in Oslo: a capital where the metro ends in a forest

Both of the afternoon's stops are in Bjørvika, the reclaimed harbour behind the station, so you can drop bags and walk. The Munch museum opened in 2021 in a tower that leans forward over the water and was thoroughly disliked when the drawings were published. It holds the enormous collection Munch left to the city in his will, over a thousand paintings and many times that in prints and drawings, spread up thirteen floors with the galleries getting quieter as you climb. He made several versions of The Scream and they are rotated rather than shown together, so which one you meet is luck.

Munch was more than one picture, and the museum is where that becomes obvious: the sickroom paintings, the frieze of life series, the late self portraits made in his seventies with the same unflinching attention. Give it two hours and take the lift to the top bar afterwards for the view back down the fjord.

Then walk five minutes to the opera house and go up the outside of it. The building is faced in white Carrara marble laid on slopes that run from the pavement to the ridge of the roof, with no barriers, no ticket and no instruction not to. It won the Mies van der Rohe prize in 2009 and it is still the most generous piece of public architecture in Scandinavia: a national institution whose roof is a public square. Go at sunset.

Bygdøy is a wooded peninsula ten minutes across the water, and Norway keeps most of its national story on it. Take the boat from behind the City Hall rather than the bus. Three museums are worth the day and they are ten minutes' walk apart.

The Fram is the one to see first, because nothing else is quite like it. Nansen had it built in 1892 with a rounded hull designed to be squeezed upward rather than crushed when the pack ice closed on it, deliberately froze it into the Arctic ice and drifted north for three years to see where the current went. Amundsen then took the same ship south and left from it for the Pole in 1911. It is indoors, complete, and you can go aboard and down into the cabins, which are smaller and darker than any account prepares you for.

Next door, the Kon-Tiki museum has Thor Heyerdahl's raft, nine balsa logs lashed together, which he and five others sailed four thousand miles from Peru into Polynesia in 1947 to argue that the Pacific could have been settled from the east. Most archaeologists think he was wrong. It remains one of the most audacious things anybody has done on purpose, and the raft in the room is very small.

Finish uphill at the Norwegian Museum of Cultural History, an open air museum of some hundred and sixty relocated buildings including the Gol stave church, a wooden church from about 1200 with dragon heads on the gables, moved here in the 1880s. There is also a reconstructed town street where each apartment is furnished to a different decade from the 1850s to the 1980s, and the last one, a Pakistani Norwegian family's flat from 1979, is quietly the best thing in the place.

Gustav Vigeland spent the last twenty years of his life on one commission and the city gave him a park to put it in. Frogner park is free, open at all hours and holds roughly two hundred figures in bronze, granite and wrought iron, all of them naked, all of them by him, arranged along an axis that climbs to a seventeen metre monolith carved from a single block of granite with a hundred and twenty one bodies twisting up it. It is not a subtle work. It is also unforgettable, and there is nothing else quite like it in Europe.

The pieces people photograph are the small ones on the bridge, particularly the toddler in mid tantrum. Children climb the statues and nobody stops them. Give it a couple of hours and walk down to the museum at the south end afterwards, which was Vigeland's studio and his home, given to him by the city in exchange for the entire contents of it after his death. His ashes are in the tower.

In the afternoon take the metro on line 1 towards Frognerseteren. It climbs steadily out of the city and by the time it reaches Holmenkollen you are four hundred metres up and in trees. The ski jump has been rebuilt more than a dozen times since it opened in 1892 and the current steel one dates from 2010; a lift takes you up the tower, from where the drop reads as considerably worse than it looks from below, and the world's oldest ski museum is dug into the hill underneath it.

Stay on to the end of the line for waffles with sour cream and cloudberry jam at Frognerseteren, in a dragon style timber lodge from 1891 with the whole city and fjord below it. In winter the trails start at the platform.

The National Museum opened in 2022 and swallowed four older institutions, which makes it the largest art museum in the Nordic countries and, on the second floor, a straightforward walk through Norwegian and European painting from the fifteenth century to now. There is a room of Munch in it, including one of the painted Screams, and the Norwegian romantic landscape painters in the rooms before it are the reason half of the country's tourist industry exists. The ground floor covers design and architecture. It is ten minutes from the station.

Then walk east along the water to Akershus, the fortress on the headland, begun around 1300 and never taken by a besieging army. The grounds are free and open late, the ramparts look straight down the fjord, and the castle inside holds the royal mausoleum and a set of dark stone halls you are allowed to wander through without much supervision. The resistance museum in the old arsenal is small and worth the twenty minutes: this is where the German occupation authorities executed Norwegian resistance members, and where Quisling was shot in 1945.

Oslo Central Station is a ten minute walk from the fortress gate, and the airport trains leave every ten minutes.