Travel review: Copenhagen, Denmark

But there is a hip, multicultural side to Copenhagen that is getting it a reputation as one of the up-and-coming destinations for city-breakers.

The multicoloured waterfront town houses of Nyhavn, Tivoli Gardens (the second oldest theme park in the world plonked in the heart of the city) and the dockside statue of Hans Christian Andersen's Little Mermaid at Langelinie are all well known. Just a short stroll, however, and you are into a more modern world of cutting edge eateries, boutique shops and forward-thinking design in the hip Vesterbro district and cultural melting pot of Norrebro.

I arrived in Copenhagen in the middle of a heat wave, instantly confounding my expectations of the Scandanavian city, but there were plenty more surprises in store that had nothing to do with the weather. It takes a while for it sink in what is different about the urban experience in the Danish city – clean air, an unhurried pace and lack of congestion (of both cars and pedestrians) is normal throughout the city centre.

Bikes are king in Copenhagen – there are nearly twice as many as people, while car ownership is less than half the population.

You can grab an electric bike off the street at ranks everywhere in the city centre, and the idea is inviting rather than intimidating – the bike lanes are often the same width as the main carriageway, and every bit as well-connected and as thought out in an unprecedented commitment to get people out of their cars and onto the pedals.

It is not just bikes that are making Copenhagen greener in its aim to become the first carbon-neutral city by 2025, with recycling bins on the streets and evidence of re-used 'upcycled' materials everywhere, from fences full of plants growing in old drink bottles to the proliferation of city-centre flea markets.

Nowhere is this more in evidence than in multicultural Norrebro, its streets decorated with equal parts graffiti and greenery, with plenty of quiet little green spaces created where its densely packed 'back houses' were demolished in the 1990s. It also boasts Assistens Cemetery, the final resting place of Hans Christian Anderson, which doubles as a public park the size of 26 football pitches.

Sine Schmidt, who offers visitor tours around the district with Cph:cool, says: "You can always find a little place to sit and have a quiet moment or enjoy a picnic with friends and neighbours, and it also cleans up the air in downtown Copenhagen. The city has been changing a lot over the last 10 years. Before it was about going to see Tivoli Gardens, and seeing the Little Mermaid and people thought that was it, you've done it."

She says the streets of the district used to be known for gangs but were now well integrated and family friendly, with some, such as Jagersborggade, showing a radical transformation. "In the 1990s this was the place where you would go to get drugs," she says, "there were dealers hanging out on these streets and it was a bit 'spooky' – it wasn't where decent people would go. The people who lived here decided, why not just put all the apartments together and form one big condo – and together they were strong.

"They worked with the police for years to get rid of the drug dealers. People live here with their families now and take their children to play parks here."

Jagersborggade is now one of the hippest streets in the city, boasting a vast array of quirky boutique shops selling everything from with liquid-nitrogen ice cream to hand-crafted ceramics, and even has Michelin-starred restaurant Relae and its affordable sibling Manfreds across the way.

She says 'grass roots culture' was still very important in Norrebro, with even Danish chains facing a hostile reception from locals while independent shops and microbreweries were on the rise. Brus Bar on Guldbergsgade is one example of a craft-ale brewery opened just months ago in a former locomotive factory, by two friends who started brewing in a kitchen classroom at school.

Sine says: "Very recently this area was turned into an area where you can explore and have good food.

"In the 1990s there were two French cafés along here, but they were about the only places you could go and get a beer, so it has really changed."

Brus Bar proved such a hip concept in such a lively district that it also attracted Christian Gadient, the city's youngest Michelin-starred chef, to jump ship from the D'angleterre Hotel just moments after earning his star, to start Spontan restaurant under the same roof. Dining out is a big deal in Copenhagen, and a similar story of a working class area becoming the place to go for food and drink is Vesterbro's Meatpacking District, a strange combination of still-functioning meat industry and trendy bars, brew-pubs, eateries and art galleries, all jostling together in a complex of white industrial-looking buildings around a huge courtyard.

Prices vary from budget to high end, but even fine dining is in reach with places such as the un-fussy Restaurant Gorilla offering a whopping 10-course taster menu including oysters, octopus, shrimp radiatore and a beautiful beef brisket for just DKK 375 (about £40) per head.

Once Copenhagen's infamous red light district, Vesterbro is now one of the most fashionable places to eat, shop and live in the city, with streets lined with hip cafes, serving iced lattes alongside vinyl records and such like, all just a five-minute walk from Copenhagen's Central Station.

The main drag of Vaernedamsvej has often been compared with the streets of Paris for its street-spilling cafe culture, with the 1950s-themed Granola perhaps the most famous of its eateries serving traditional Danish open-faced sandwiches, or smorrebrod, with a delicious variety of toppings, just down from the equally charming Central Hotel and Café, which with just one cosy room, is the world's smallest.

Our guide to the district, Henrick Thierlein of Wonderful Copenhagen, said: "We used to say it was like a bit of Paris in Copenhagen but now we are so famous we don't have to say that anymore – we ARE the Paris of Scandinavia."

All in all, for the Brit abroad, Copenhagen is a fascinating mix of the familiar and the inspiringly fresh.

One of my London-based companions on our trip was bowled over by the city's hipper downtown districts, summing it up as: "What I want London to be like, desperately – but know it's never going to be."