Surrounded by sea, peppered with sleek and striking architecture, and populated by an attractive, laid-back bunch of Danes, Copenhagen tops the table for being Europe’s most relaxed city. But this enviable lifestyle comes at a cost – it’s also one of the most expensive cities you’ll ever come across.  With food and drink at eye-wateringly high prices, you’ll need a wad of cash to sustain yourself, but follow these tips for free things to do in Copenhagen, and maybe you could afford that trip to Noma after all…

Visit the Little Mermaid

Copenhagen’s biggest – and smallest – icon, the Little Mermaid is a diminutive statue sitting at the end of the Langelinie promenade. Commissioned in 1909 by the founder of the Carlsberg brewery, J. C Jacobsen, and unveiled in 1913, the poor little soul has been subjected to vicious vandalism over the years, having had her head and limbs chopped off, had paint thrown over her and even been bombed in 2003. It’s free to go and pay her a somewhat more deferential visit.

The Little Mermaid, Copenhagen

Picnic in the Kongens Have

Laced by leafy avenues and spread with lush green grass, the Kongens Have is Copenhagen’s oldest and most popular public garden – and makes the perfect spot to hunker down in the shade with a tasty picnic. In the height of summer there are puppet shows and free music concerts to accompany your sandwich.

Jump on a bike

Launched in 1995, Copenhagen was the very first city to offer free bikes to the public. The scheme is still going strong today – and with most of the city centre given over to pedestrians and cyclists, it makes for a pleasant, stress-free ride. At one of the 110 bike racks available, pop a 20DKK or €2 coin in the machine, pootle around on your bike, and when you’re finished you’ll get your coin back.

Swim in the Islands Brugge

In the summer months (June–Aug), plunge into the clean, fresh waters of Islands Brugge, a fashionable harbour-front swimming pool, just near the city centre in Indre By.

Museum-hop for free

Free museums in Copenhagen include the National Museum, National Gallery and Danish Resistance Museum. Others, such as the Ny Carlsberg Glyptotek and the Hirschsprung Collection, are free for one day during the week – usually Fridays.  You’ll get plenty of culture for free here.

Copenhagen National Gallery

Hit the beach

With so much sea water around, it’s not surprising that Copenhagen has a clutch of fine-looking beaches: Amager Strand (5km from the centre; take the metro to Amager Strand or Femøren, or bus #12), Bellevue Beach (S-train to Klampenborg Station) and Charlottenlund (bus #14) are long swathes of powder-white sand lapped by invitingly clear, blue water.

Wander round Christiana

A former barracks colonized by hippies and controversially declared a “free city” in 1971, Christiana sits to the west of the city centre, in the borough of Christianshavn. Colourful, quirky buildings house small businesses, theatres and cafés. There are guided tours around the area, for which you have to pay, but it’s free to stroll round by yourself; just refrain from taking photographs.

Christiana district in Copenhagen

Catch a film outdoors

Film-lovers will be in seventh heaven during the summer months, when there are screenings of classic and contemporary films – both Danish- and English-language – in a variety of the city’s parks most evenings. Bring a blanket, a bottle of wine and perhaps some popcorn.

Watch the Changing of the Guard

Home-sick Londoners might want to head to the Amalienborg Castle on the harbour front to watch the Changing of the Guard – or “Vagtparade” in Danish – which takes place at noon every day. Expect blue trouser-clad soldiers marching round to rousing music, bellowing orders.

Changing of the guard, Copenhagen

Party with the locals

Copenhagen’s festival calendar is absolutely jam-packed during the summer. There are free jazz concerts, fashion shows, dance performances, art exhibitions, city walks, Copenhagen Gay Pride (mid-August), sports matches - the list goes on. Most atmospheric are the Midsummer Night’s Eve celebrations in June, when hundreds of bonfires are lit in various spots in and around the city, crowds feast on barbecued meat and everyone enjoys a great big sing-song.