Not so long ago its principal claim to fame was a tiny mermaid and the fairytale harbour which enchanted her creator, Hans Christian Andersen. But since the Danes started making headlines with their edgy fashion, modernist furniture, futuristic architecture and award-winning food, Copenhagen has leapt into the top tier of world-class cities.

This is a great year to visit — or revisit — the Danish capital, with Noma, repeatedly voted world’s best restaurant, reopening in a new location and breathtaking new attractions like Copenhill, an artificial ski slope audaciously perched on a sloping power station roof.

New hotels have opened too, while the city’s best is presenting a fabulous new face following extensive building work.

What would Andersen, who would nowadays be peering across the harbour at Copenhill on his daily stroll, have made of the transformation of the quaint mediaeval streets into edgy city-break metropolis?

No doubt he’d have written a story about it, as his successors have done with their Scandi noir thrillers set in streets now more modish than mean.

Like those of the city’s meat-packing district, whose former slaughterhouses have metamorphosed into fashionable bars and restaurants, working-class districts like Vesterbro which have regentrified and the formerly desolate, no-man’s island of Refshaleoen, nicknamed Reffen, which is today’s hottest new area in which to work, play and dine.

First-timers should still start at the picturesque harbour, Nyhavn. The cobbled quays lined with tall pastel-painted houses, two of which were home to Andersen at different times, are picture postcard pretty, especially in the afternoons.

It’s also the place to embark on a harbour cruise, whose boats navigate the city’s inland waterways and give a good overview of this Scandinavian Venice, although you could walk to The Little Mermaid herself along the harbourfront — surprisingly small for such an icon.

Fans of cutting-edge architecture will want to cross the new pedestrian bridge and walk along the waterfront to the city’s major road bridge, where the National Library extension known as the Black Diamond sits on its own stretch of water.

A few steps away, the green and white glass blocks of Blox — the brand-new Danish Architecture Centre — brings exciting, double-height exhibition spaces to the city, including an opening show focusing on how Denmark lives today.

Not far from this futuristic face of the city, you can also find the Jewish Museum, housed in the royal garden complex. Designed by Daniel Liebeskind, and as disorienting as his larger counterpart in Berlin, it tells a happier tale.

Uniquely among countries under Nazi occupation, 99 per cent of Denmark’s Jewish population survived the war, thanks to the country refusing to give up its Jews.

A round-up action was planned, but the Danes got wind of it in time to organise a Dunkirk-style evacuation to safety across the sound in Sweden. Some stayed there, but the community has been boosted by a postwar emigration wave of Polish Jews seeking a more tolerant society.

Further north, the Experimentarium, re-opened last year, might be aimed at children but even adults will thrill at the 10-ton double helix copper staircase.

For a hotel with as much style as the city, there’s no architecture to beat The Nimb. A model of Danish modernism on the side facing the station, there’s no stripped-back Scandi styling to be found here except in the amazing high-ceilinged bar.

Instead, a collection of sumptuous rooms furnished with antiques, working fireplaces and some of the most luxurious hotel bathrooms in the world. Yet the main attraction is outside the bedroom windows — the Tivoli Gardens, Copenhagen’s top attraction, to which admission is free, rides and all, for Nimb residents. And the hotel’s rear façade, facing into Tivoli, is an attraction in itself — a Moorish palace awash in fairy lights.

Until recently, it was extremely difficult to find space in the original 17-room hotel, but it more than doubled in size this year with a handsome extension that adds a rooftop terrace, pool, gym and treatment rooms.

An excellent French brasserie serves superlative breakfasts and there’s a traditional Danish smorrebrod restaurant for some classic open sandwiches.

With the new rooms sure to be in demand as well, there’s also the nearby Nobis Hotel, an old music conservatory updated with mid-century furniture; stylish if less opulent.

When it comes to restaurants, Noma remains the hottest name — and its new location is close to Copenhagen’s second most popular attraction, the alternative hippy community of Christiania.

Noma is elsewhere on the island of otherwise-respectable Christianshavn, away from this edgy and arty urban village, but requires weeks of advance booking.

There are some fine alternatives though, from The Standard, with Nordic influenced dishes served up in an old Art Deco customs house complete with waterside views on the untouristy far side of Nyhavn.

Or you can find Michelin Bib Gourmand quality in a more light-hearted setting at Fiskebaren, a super fish restaurant in the meat-packing district, or its sister, Musling Bistro, opposite the Torvehallerne food hall at Norreport.

The fairytale city might have a more futuristic face, but whether you prefer the traditional or the new, wonderful Copenhagen hasn’t lost its allure.