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How to indulge in Copenhagen on a budget

Strolling down Vaernedamsve, a picturesque street between the former red light district of Vesterbro and the fashionable municipality of Frederiksberg, I feel smack bang in the middle of chic Scandi living. There are hipster coffee hangouts, minimalist plant shops and impossibly cool interior stores, with bikes artfully propped against lamp posts.

Copenhagen is remarkably calm for a capital. The majority of people ride bikes rather than drive cars and everything feels cosy, content and stress-free. The Danes even have a word for it, of course - hygge.

The city, which is less than a two-hour flight from London, also has a buzzing food scene, with several new restaurant openings every month. But with 15 Michelin star restaurants, including Noma, which was named the best restaurant in the world four times, it has a reputation for being pricey.

Plan carefully, though, and you can have an affordable weekend break. Here's how to get the most out of the city while keeping the costs down...

1. TAKE IN THE VIEW AT CHRISTIANSBORG PALACE

The 360-degree views from the Danish Parliament building, the tallest tower in Copenhagen at 106 metres (they don't do skyscrapers here), really show off the city's juxtaposing modern minimalist and old fairy tale-like architecture.

From here you'll see the Borsen, the 17th-century stock exchange building with a spire design of four dragons' tails twisted together, as well as the Amager Bakke waste-energy power plant, where the world's longest artificial ski slope is set to open this winter. You can see all the way to Sweden on a clear day.

2. SEE THE CITY FROM THE WATER

The excellent value Copenhagen Card gives tourists free public transport by bus, train and Metro and free entry to 79 museums and attractions. Use it on a boat tour down the canals around what's known as the Harbour Circle, passing the colourful town houses of Nyhaven and enviably stylish house boats, towards the striking Black Diamond Library, Amalienborg Palace (the Danish royal family's official residency) and the famous Little Mermaid statue.

Inspired by Danish author Hans Christian Anderson's fairy-tale, the famous figure "has been decapitated twice and had her arm copped off" in various protests, according to our tour guide.

3. HIRE CITY BIKES

The city is small enough to walk everywhere, but if you want to fit in with the Danes, you need to hop on a bike. There are thousands of Bycyklen - electric bikes with built in GPS to guide you - found at docking stations dotted around the city. Simply register online with a credit card to pay as you go before picking up a bike.

And you'll be in good company; at the last count there were 265,700 bikes in Copenhagen. Strangely, no one appears to wear helmets (there's no requirement by law) but the roads are very bike friendly with cycle lanes and four bike-only highways.

4. SHARE A SMORREBROD

You can't go to Denmark without having an open sandwich - it's a Danish staple. Head to Din Nye Ven in Indre By, a laid-back and effortlessly cool cafe, for smorrebrod with toppings such as mackerel and smoked cream cheese or avocado piled high on rye bread, all traditionally washed down with Danish beer, like Pilsner or Mikkeller, and schnapps. The generous portions of good quality ingredients will keep you going for a busy day of sightseeing.

5. TAKE ADVANTAGE OF THE FIXED PRICE TREND

Lots of the city's restaurants offer good deals if you book multi-course meals - so the more you eat, the better value you can expect. The trendy Norrebro district is known for it's gastronomic offerings and there's a huge focus on clean, sustainable, organic and foraged food.

Head to the waterfront branch of the Madklubben chain at Norrebro, which serves unpretentious hearty dishes such as delicate-as-you-like whole sea bass, flame-grilled cauliflower with salted almonds, and a seriously addictive spiced mash with sour cream. It's packed every night (as with any restaurant in Copenhagen) so you'll need to book ahead.

6. DISCOVER COPENHAGEN'S ART SCENE

A 40-minute train ride from the central station, overlooking the Oresund Sound in Humlebaek, is the Louisiana Museum of Modern Art, where permanent exhibits include Alberto Giacometti's distinctive elongated bronze figure sculptures. What most people really come for, though, is the wonderful sculpture gardens and lunch of fresh, seasonal Danish produce overlooking the river.

7. BECOME A KID AGAIN

A trip to the Danish capital wouldn't be complete without stepping foot inside the Tivoli Gardens, which dates back to 1843. You don't find many amusement parks smack bang in the middle of a city, but the second oldest in the world, Tivoli, is a charming Danish institution.

Here you'll find one of the world's oldest wooden roller-coasters, Rutschebanen (which is faster than it looks) as well as The Demon, a more modern loop-the-loop, where riders wear a virtual reality headset.

Don't miss out on lunch at new restaurant Gemyse in the gardens - where vegetables take centre stage, sustainability is a priority and you can eat in a greenhouse filled with growing herbs.