Two years ago this month, the members of Abba were pictured together for the first time since 2008, fuelling rumours that a reunion was on the cards. They were at the opening of Mamma Mia! The Party, a new Stockholm restaurant decked out like the Greek taverna in the film Mamma Mia! Here you can eat your hummus and pretend you’re an extra in the movie as live singers and musicians serenade you with Abba songs.

At first glance, I thought the restaurant was a theme park when I passed it on my way to the Abba museum.

This is a treasure trove of memorabilia, stuffed into the basement of the aptly named Pop House Hotel, that charts the rise and rise of the supergroup. Although Abba split in 1982 they live on through savvy investments like this museum and its merchandise, the stage shows and films – the sequel Mamma Mia Here we go again is due to be released in July. They also have a world tour planned for 2019. Before you get too excited, Agnetha, Bjorn, Benny and Anni-Frid won’t be setting foot outside Sweden. Instead, their digital avatars will wing their way around the globe.

I suspect the idea for a hologram Abba developed from one of the most popular interactive exhibits at the museum; your chance to "appear" on stage alongside Abba in Dancing Queen. How could I resist it? I lined up with the life-like holograms and tried to follow their steps. Thanks to modern technology, I can be embarrassed all over again by accessing a recording of my efforts on the museum’s website via my ticket number. You can also sing-along with Abba and pretend you’re mixing some of their soundtracks as part of a re-creation of the Polar Studios where they recorded all their albums. Unfortunately the day I visited the museum the English versions weren’t working. Probably just as well.

There’s enough personal Abba paraphernalia packed into the museum to keep fans happy for decades. For instance, the white piano from the cottage on Viggso in Stockholm’s archipelago where Bjorn and Benny went to write is there, as is a replica of Bjorn and Agnetha’s kitchen with a radio by the sink playing Slipping through my Fingers – the heart-breaking song Bjorn wrote after watching his daughter going off to school – and the red telephone from the video of the group’s first major hit song Ring Ring. Apparently only four people in the world know this phone number.

I’d heard that Bjorn sometimes visits the museum and poses as one of the models then comes to life when people walk by. Another thing I seemed to have missed. More’s the pity as the exhibition of the group’s most recognisable costumes look a little lifeless on the models. After a few nostalgic hours I leave the museum via the shop where I manage to resist buying the kit to knit yourself a blue cap, just like the one Agnetha wore when Abba won Eurovision in 1974 with Waterloo.

But there’s more to Stockholm than Abba. The Swedish capital, built on a series of islands, has a rich naval history. A stone’s throw from the Abba exhibition is the Vasa Museum. It houses the 17th century warship of the same name which sank minutes after it was launched in 1628. For 333 years it lay on the seabed in Stockholm harbour, not far from the museum, until it was found and salvaged in the 1960s. It’s a lesson in not letting a king, in this case Gustav II Adolf, dictate how to build a warship. He insisted on having not one, but two decks of canons. The top-heavy vessel also didn’t have enough ballast, so it keeled over only a few yards from where it was berthed. Fifty-three of the people on board were drowned.

Apart from the warship itself – it’s an impressive 172ft high and 226ft long – there are fascinating exhibits on its salvage and preservation as well as several videos. I was riveted by the recreation of the trial after the Vasa sunk which features actual testimonies from those involved, expect for the king. Skeletons and everyday items such as coins, spoons and games are also on display. They give a colourful view of what life on board the ship must have been like. It’s ironic that if the ship hadn’t sunk and been preserved in the muddy seabed, it would not be here now.

The life-size, and incredibly life-like, models of the people associated with the Vasa, many of them women, further enhance the warship’s story. It appears these 17th century women had more power and influence than you might think. After her husband died, Margareta Nilsdotter took over the running of the shipyard that built the Vasa while Brita Gustafsdotter Bath supplied the timber used for its construction. Then there was Yiva and Beata who were both on board the Vasa when she sank. It’s thought that Beata was a guest so she could have been the sister or wife of a crew member. Of the many objects salvaged from these women’s lives, it was their tiny shoes that I found the most poignant.

Stockholm’s old city, Gamla Stan, on the island of Stadsholmen is where Sweden’s capital was founded in 1252. The Royal Palace with its homage to Versailles – the Great Hall of Mirrors – dominates what is one of the largest and best preserved medieval city centres in Europe. With its narrow closes and cobblestones, Gamla Stan is a bit like Edinburgh’s Old Town and it’s easy to get lost in the maze-like passages. So I completely missed the narrowest street, Marten Trotzig’s alley. Only 90cm wide at its narrowest point, it’s apparently no more than an arm span. But I did come across the Nobel Museum in the former Stock Exchange building. Here you can find out more about Alfred Nobel, the Swedish chemist who invented dynamite and left his fortune for the prize, as well as the hundreds of laureates who have been awarded the prize since it was set up in 1901. The museum’s due to move to a new centre, designed by David Chipperfield, on Stockholm’s seafront in a few years. In the meantime, all the Nobel Prize ceremonies continue to take place in the city’s concert hall.

Outside the concert hall is a large sculpture, the Orpheus Fountain, by Swedish artist Carl Milles. It’s well worth the 20 minute journey out of town to visit Millesgarden, the stunning home and sculpture garden that belonged to Carl and his wife Olga, who was also an artist. It’s on the island of Lindingo overlooking the terminal where cruise ships leave for the Baltic.

The house itself is a labour of love with Carl and Olga putting it together bit by bit themselves. They spent their evenings lying on the floor gluing tiny grey and black tiles down to create a gorgeous mosaic. Their striking wooden chairs were made out of the yokes oxen wore to plough the fields. And of course artworks by the couple and Olga’s sculptor sister Ruth are scattered throughout the house alongside other paintings and items the family collected over the years.

But it’s Milles’ huge bronze sculptures that dominate the skyline in the outdoor courtyard. His figures seem to float on air, perched high up against a backdrop of blue sky balanced on nothing more than a toe or, in the case of one of his most famous works The Hand of God, a thumb and finger. At ground level there are fountains filled with sprites, nymphs and muses. My favourite water sculpture is of a naked woman riding a dolphin as if it were a bucking bronco, her hair streaming wildly behind her. I could have spent a whole day at this museum and more than a few days in this entrancing summer night city.

Travel notes

Getting there

Norwegian (norwegian.com) fly Edinburgh to Stockholm direct from £120 and KLM (klm.com) fly there from Aberdeen, Edinburgh and Glasgow via Amsterdam from £170.

Where to stay

Prices range from £750 a night at the Lydmar to £93 a night at the Radisson Blu on the waterfront. For something cheaper and quirkier, there’s the Red Boat riverside hotel and hostel from £40 a night.

Other information

Go to visitstockholm.com. The Stockholmpass.com is worth getting if you’re going to a lot of paying attractions.