Never mind the Vikings, Stockholm is a city designed for children. The days of rugged bearded men and plunder are over; today, this is a city of gentle, safety-conscious people.

You need only look at a zebra crossing and the cars screech to a halt.

There is something for children around every pretty corner, such as an impromptu street performance or a horse-drawn carriage trundling its way up the cobbled streets of the old town. Even the national dish, hot dogs and meatballs, is reminiscent of nursery food. For hungry little ones, this is paradise. Several times a day, the whole country stops for a snack, which involves a kanelbulle (cinnamon bun) or a round cocoa cake rolled in desiccated coconut.

Stockholm is clean, well organised and extremely child-friendly!

There is no better example of this than Djurgarden, an island in the centre of town almost entirely dedicated to children’s pleasure. There is an amusement park, several museums, countless hot dog and icecream stands and even a zoo.

One of the main attractions is Junibacken, which describes itself as a living fairy-tale house. It is full of characters from Swedish children’s books, the most famous of whom is Pippi Longstocking.

The highlight of the visit is the fairy-story train. It is more like a magical wooden chair, but it whisks you around scenes from children’s books, all beautifully presented.

Even my husband (who couldn’t tell Pippi from a troll) was impressed; the children were enthralled. Remember to ask for the tour in English.

And after all the fun and frolics, the cafe offers lots of home-baked Swedish goodies. If it’s sunny, sit outside and watch the boats glide by.

In fact, the nicest way to get to Djurgarden is by ferry. It costs less than a London Tube fare and boats depart every 20 minutes from Nybro Square.

Buy the Stockholm Card (stockholmtown.com/shoponline) and you’ll get into 75 museums free with all your transport thrown in, too.

A short walk from Junibacken, there are two more must-sees.

At the Nordic museum (nordiskamuseet.se), the children will love the reconstruction of a old farmyard, where they can milk wooden cows and pull themselves across a plastic river on a wooden barge. My husband lost the will to live after an hour, but the rest of the family were happy.

Stockholm’s most famous museum is the Vasa (vasamuseet.sr), built around a regal ship that sank on its maiden voyage in 1628 and was then salvaged from the depths. The Vasa is the only intact 17th century ship in the world.

If you are lucky enough to get a sunny day (not always a given in Stockholm), head for Skansen (skansen.se/eng), an open-air museum and zoo. As well as animals (most popular are the seals, who perform water acrobatics), you can see Swedish buildings from the 18th, 19th and 20th centuries.

More than 150 houses were transported to Skansen from all over the country. Staff in traditional costume tell you how people used to live. Grona Lund, Sweden’s most famous amusement park, is next door to Skansen. Unlike many theme parks, there is no foul-smelling food and lots of trees give a park-like atmosphere.

As for the rides, don’t bother with the ghost train. And if you are tempted by the human falling elevator, my advice is to try the children’s version first (more than enough for me). The Ladybird rollercoaster is a must.

Back in the centre of town, Kungstragarden is a great place to eat. The children can play on the brass lions and jump up and down on trampolines while you enjoy an aperitif.

The Victoria restaurant is famous for its meatballs with mashed potato and lingonsylt, jam made from lingonberries (or cowberries as they’re also known). Children love it.

‘This was a good idea,’ was my son Leo’s reaction when his plate arrived. By the end of the week, however, we were all longing for something else to eat.

If you’re staying at the swanky Grand Hotel (S. Blasieholmshamnen 8; 00 46 (0) 8 679 3560; grandhotel.se) and money is no object, book the newly refurbished Mathias Dahlgren restaurant on the ground floor designed by the British designer Ilsa Crawford.

You can leave the children with a hotel baby-sitter for £22 an hour.

Kids are well catered for on the island of Djurgarden

Stockholm has more museums per square mile than any other European city, but even if you miss most of them, you simply can’t leave without a visit to the Modern Museum (modernamuseet.se).

It is one of the best-designed museums I have visited; the spaces are large and light, and the exhibitions small enough for youngsters to take in. If you time your visit right, the children can go on an art tour with a member of staff followed by a visit to the museum studio where they can paint for hours on end. The only downside is that you have to go with them.

Once you’ve had enough of traipsing around town, you can head to the beautiful Stockholm archipelago.

Take the boat from opposite the Grand Hotel and, if you’re lucky enough to get one of the old-fashioned ships, check out the cafe with its fin de siecle red velvet chairs and linen napkins.

Just don’t eat there  –  the food is not great. Go for a punschrulle (a marzipancovered cake) or kanelbulle from the bar instead.

The Stockholm archipelago is made up of more than 25,000 islands. One of the loveliest is Grinda, just an hour by ferry from Stockholm, where you can go on a one-and-a-half-mile circular walk around the island.

There, you’ll see one of the few working farms in the archipelago (look out for lots of long-haired sheep) and you can pick wild blueberries for hours in the woods.

You could almost leave the children to explore while you have a civilised lunch at the Grinda Vardshus.

Sweden must be one of the safest countries in the world. At one point, I briefly lost my three-year-old, but found him looking jolly pleased with himself in the arms of a buxom blonde.

And if you’re flying in or out early in the morning, as we did, you should stay at Hotel Kompaniet in Nykoping (Folkkungavagen 1; 00 46 (0) 155 28 80 20; choicehotels.no), which is only a 15-minute taxi ride to the airport.

Youngsters get an activity pack on arrival and will love the sauna and whirlpool spa.

Either way, by the time we left, the children were rosy-cheeked and chuckling and we parents were basking in the Swede smell of success.