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Evidence of Copenhagen’s seafaring past is obvious at every turn in the city centre. If you’re anticipating sailors’ taverns, sea shanties and disreputable districts, however, think again. This historic quarter’s maritime heritage is evident in beautifully restored dockland warehouses, quaint quaysides trimmed with colourful houses and yacht-filled harbours.

It’s also home to grand museums and swanky restaurants, and it’s where you’ll find most of Copenhagen’s five-star hotels, many of which tower over the waterfront and offer spectacular views.

Surprisingly, cheap Copenhagen hotels in the city centre are also in abundance, with several design hostels and budget hotel brands offering good-value rooms. Which means you can still stay in the heart of Copenhagen, even if you’re travelling on a shoestring.

Copenhagen Zoo is in upmarket Frederiksberg, along with the magnificent Frederiksberg Palace and the enchanting royal gardens of the same name. This sophisticated district is just a stone’s throw from the city centre and peppered with design hotels and chic aparthotels.

Connoisseurs of cocktails will enjoy Frederiksberg’s sophisticated bars, while shoppers will love the elite boutiques and specialist jewellers on the Parisian-style shopping street of Værnedamsvej.

Long and lovely boulevards make strolling around a pleasure and the area is famous for its pretty pavement cafés too.

Lovers of the outdoors and families will find it hard to top Vestegnen, Copenhagen’s seaside district, which is just half an hour from the city centre.

Vestegnen is a magnet for weekenders escaping the city bustle and has some of the best cheap hotels in Copenhagen, from heritage guesthouses and waterfront resorts to cosy, family-suitable self-catering options.

The mightiest of all of the city’s art museums, ARKEN, is also here on Køge Bay Beach, as is the Circus Museum, where visitors can learn about famous performers and even try out a few skills – including tightrope walking and juggling. In winter, stargazers can use the powerful telescopes at Ole Rømer’s observatory in Vestegnen, where the Danish astronomer first defined the speed of light.