• Don't miss the Little Mermaid statue by Copenhagen's harbour entrance. It often surprises first-time visitors with its small size, but the commemoration of one of Hans Christian Andersen's most popular fairytale characters is widely known as the city's symbol.

• Retrace Denmark's Viking heritage at the Viking Ship Museum at Roskilde (website: www.vikingeskibsmuseet.dk), around 30km (19 miles) from Copenhagen, featuring five ancient vessels rescued from the waters of the harbour.

• Pay homage to one of the world's best-known beers at the famous Carlsberg Brewery ( website: www.carlsberggroup.com/Experience/VisitCarlsberg), which is a short train ride from Copenhagen's central station, and has an extensive visitor centre telling the story of the company and its products.

• Take in the pomp at Amalienborg Palace (website: http://kongehuset.dk), the royal winter residence in the centre of Copenhagen. It is worth being there at 1200, when the daily changing of the ceremonial guard takes place.

• Follow in the fictional footsteps of Hamlet to Elsinore (Helsingør in Danish), where the mighty 16th-century Kronborg Castle (website: www.kronborgcastle.com) watches over the waters of Øresund and the nearby Swedish coast.

• Take a walk around Christiania, Copenhagen's ‘independent' hippy community founded in 1971 to provide a home for those seeking an alternative lifestyle. As ever, it is a thorn in authority's side, but enduring as a tradition.

• Explore the largest-remaining Viking burial site at the city of Ålborg, which also counts a castle, a cathedral and a monastery among its attractions, and is the home of a well-known variety of akkevit spirit (a spiced schnapps-type drink). 

• In summer, do as the Danish royal family does and take a trip to Århus. Their summer residence is the Marselisborg Castle (website: www.kongehuset.dk), whose grounds are open to the public when the Queen is not in residence.

• Also when in Århus, take a stroll around the Old Town open-air museum, a collection of buildings dating from the Renaissance to WWI, and brought to the site from all over Denmark (website: www.visitaarhus.com).

• Relive childhood with a visit to the birthplace of the great fairytale writer Hans Christian Andersen in Odense. Visitors can also have a look around the Hans Christian Andersen Museum (website: www.museum.odense.dk) and his childhood home.