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  • BEST THINGS ARE FREE: Take a stroll down Stroeget for...

    BEST THINGS ARE FREE: Take a stroll down Stroeget for window shopping, catch a show during the Copenhagn Jazz Festival, or head over to Hans Christian Andersen’s grave at Assistens churchyard, top.

  • BEST THINGS ARE FREE: Catch a show during the Copenhagn...

    BEST THINGS ARE FREE: Catch a show during the Copenhagn Jazz Festival, above.

  • ART AND LITERATURE: Take in an art museum such as...

    ART AND LITERATURE: Take in an art museum such as the Statens Museum for Kunst, above, or seek out the city’s literary history with such sites as the Little Mermaid statue, right.

  • BEST THINGS ARE FREE: Take a stroll down Stroeget for...

    BEST THINGS ARE FREE: Take a stroll down Stroeget for window shopping, above.

  • FILE - This is a April 16, 2010, file photo...

    FILE - This is a April 16, 2010, file photo of the Queen's Cavalry Squadron, passing down the shopping street Stroeget in Copenhagen, Denmark, during celebrations of Queen Margrethe's 70th birthday. (AP Photo/Polfoto/Niels Hougaard,File) DENMARK OUT

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COPENHAGEN, Denmark — While it’s easy to spend a fortune in Copenhagen, one of Europe’s most expensive cities, the Danish capital also has a lot to offer for travelers on a tight budget.

The city center is compact enough that you can get around on foot, enjoying the top sights and walking in the footsteps of fairy-tale writer Hans Christian Andersen — without spending a single krone.

Window shopping

Danes are a relaxed bunch, and shopkeepers won’t sneer at you for inspecting their goods without buying anything. There’s no place for window shopping in Copenhagen like Stroeget, the artery that runs from City Hall square to the picturesque harbor of Nyhavn. Skip the souvenir shops with plastic Viking helmets (history check: Real Viking helmets didn’t have horns) and explore the internationally acclaimed world of Danish design, from the hand-painted china at Royal Copenhagen to the cutting-edge fashion boutiques with clothes from homegrown designers like Noir, Munthe plus Simonsen, Day Birger et Mikkelsen and Baum und Pferdgarten. If you visit in December, don’t miss the Yuletide markets with Christmastime treats at Hoejbro Plads or Nyhavn.

Free museums

Take advantage of free admission to state-run museums including the National Museum, the National Gallery or the Post & Tele Museum where you can try out a telephone with a crank handle and lift a rather heavy early mobile phone (also check out the splendid view from the rooftop cafe). The David Collection features work from Vilhelm Hammershoei and other Danish painters, and a rare collection of Islamic art. Admission to the permanent collections is free, but there is a fee for temporary exhibits. Some private museums offer free access on particular days: On Mondays at Ny Carlsberg Glyptotek — best known for its impressionist paintings, antique sculptures and Etruscan collection; on Wednesdays the Danish Design Center (5 p.m.-9 p.m.) and on Fridays, the Museum of Copenhagen.

In Hans Christian Andersen’s footsteps

The 19th century author of “The Little Mermaid,” ‘’The Emperor’s New Clothes,” “The Ugly Duckling” and other fairy tales was born in central Denmark but lived and died in Copenhagen. The city has two statues of him: one in the Kongens Have park and another, more famous, outside City Hall. The Magasin du Nord department store has kept a tiny attic room where he briefly lived, and access is free through the store. His tombstone is located in the Assistens churchyard, a half-hour walk from downtown close to the graves of other famed Danes — including Danish thinker Soe­ren Kier­kegaard and Nobel Prize-winning physicist Niels Bohr. And while at that churchyard, don’t miss the grave of Giertrud Birgitte Bodenhoff, whose story is rather scary: Legend has it she was buried alive at age 19, and strangled by a grave robber shortly after her burial.

Photo souvenirs

The location of the iconic Little Mermaid statue is a bit off, and be advised: Her size is underwhelming. Still, many find her worth the half-hour walk from the downtown area. A tribute to Andersen’s fairy tale, the 100-year-old bronze statue is free to admire and photo­graph. Unfortunately, the easy access has also led to acts of vandalism. Over the years she’s been decapi­tated, splashed with paint and defaced by graffiti. Those looking for an exotic twist to their photo album or social media may want to pay a visit to Christiania, the free-wheeling neighborhood founded by hippies in the 1970s (just don’t photograph the drug dealers). The Royal Life Guards parade through the city every day at noon in connection with the changing of the guards at the Amalienborg Palace, the home of the royal family. Check out the City Hall’s ornamented front and the gilded statue of city founder Bishop Absalon just above the balcony. The building from 1905 was inspired by the City Hall in Siena, Italy, and can be visited for free.

Festivals

Copenhagen was home to a prominent jazz scene in the 1960s and 1970s, when many American jazz musicians settled here. The annual jazz festival still draws big names in early July, and many concerts are held outdoors, rain or shine. Many are free. The Kongens Have park offers a free children’s version of the festival. The park also has an old-­fashioned puppet theater during the summer months. In August, the Copenhagen Dance Festival is staged at the police headquarters from 1924, considered a masterpiece of neo-classical architecture with a circular courtyard sur­rounded by pairs of columns.