Oslo.

Akershus Fortress

Start here. You've literally parked next to it. The fortress has guarded the harbour since the Middle Ages, the grounds are free, and the walls give you the best free view of the fjord in town. Walk the ramparts on the harbour side and you'll see your ship from above.

City Hall and Aker Brygge

Don't let the outside fool you. The big brown brick box is where the Nobel Peace Prize is handed out every December, and you can walk straight in for free. The main hall is covered in huge, colourful murals of Norwegian history. Then follow the waterfront west to Aker Brygge and Tjuvholmen for coffee by the water.

Fun factThe towers hold 49 bells, from 4 tonnes down to 14 kilos, and they play a tune every hour from 7 am to midnight. In June, July and August there's a live carillon concert on Sundays at 3 pm.

Opera House roof

My favourite free thing in Oslo. You're allowed to walk all the way up the sloping white roof, and nobody will tell you off. At the top you get the fjord, the islands and the Barcode skyline in one view. Wear shoes with grip if it has rained.

Fun factLook out into the water next to the Opera. That glass and steel iceberg is a sculpture called She Lies. It floats on a platform and slowly turns with the tide and the wind, so it never looks quite the same twice.

Nobel Peace Center

Right across the square from City Hall, in the old Vestbanen railway station. The exhibitions tell the stories behind the Peace Prize winners, and they're often more moving than you'd expect. Entry costs money, but the gift shop is free and worth a look on its own.

Deichman library, right next to the Opera

Our main public library is free, warm and seriously good looking inside. Perfect if it starts to rain, and it's only a two minute walk from the Opera.

Fun factInside is a room holding sealed manuscripts by authors like Margaret Atwood and Karl Ove Knausgård. Nobody is allowed to read them until 2114. A forest of 1,000 trees was planted outside Oslo in 2014 to make the paper they'll be printed on.

MUNCH museum

The tall leaning building next to the Opera, and the reason a lot of people come to Oslo. It's packed with Edvard Munch, from the famous to the strange. Adult tickets start at 200 kroner, and you should book a time slot ahead on busy days.

Fun factThe museum owns eight versions of The Scream, and only one is out at a time. The painting, the drawing and the print take turns during the day, because light slowly damages them. So which one you see is pure luck.

Fram and Kon-Tiki museums on Bygdøy

If you have a long stop, do this. Fram is the actual polar ship Nansen took into the Arctic and Amundsen sailed south on his way to the South Pole, and you can walk around on board. Next door is the balsa raft Thor Heyerdahl sailed across the Pacific. Kids love it, and so do grown men who pretend they're there for the kids.

Vigeland Sculpture Park

More than 200 naked stone and bronze people in Frogner Park, all made by one slightly obsessed sculptor, Gustav Vigeland. Babies, grandparents, wrestling men, a 14 metre column of bodies. Free, open all year, and properly strange in the best way. Tram 12 takes you there from the centre, or hop on the sightseeing bus. Rather walk? It's about 45 minutes from the quays, and the route is half the fun: up Karl Johans gate to the Royal Palace, through the Palace Park, then along the shopping streets Hegdehaugsveien and Bogstadveien to Frogner Park. Take the tram back to save your legs.

Ekeberg, where The Scream was born

This is my insider pick. The hill above the city is the exact view Munch painted in The Scream, with the fjord and the city below. There's a sculpture park in the woods with works by artists like Salvador Dalí, and almost no cruise passengers find their way here. Take tram 13 or 19 from Oslo Central Station to the Ekebergparken stop.

Holmenkollen ski jump and ski museum

Norwegians take skiing very seriously, and this is our cathedral. Take metro line 1 up the hill, walk the last steep bit, and look down the jump. You'll understand why we think ski jumpers are slightly mad.

Fun factFeeling brave? There's a zipline from the top of the jump tower. It's 361 metres long and drops 107 metres, and you pay for it at the top.

A swim at Sørenga sjøbad

Bring swimwear. Just past the Opera there's a sea bath with a sandy beach, a 50 metre pool in the fjord and a diving tower. Locals swim here from spring to autumn, and the brave ones all winter from the pier. Nothing says Oslo like swimming in the middle of the city.

Grünerløkka and a waffle at Haralds Vaffel

The old working class area turned hip neighbourhood, with vintage shops, cafés and street art. While you're there, get a waffle at Haralds Vaffel. Try a savoury one with blue cheese or sausage. It sounds wrong and tastes right.