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Denmark may be topographically flat, but the nation is mightily uplifting in every other sense. Those regular “world’s happiest country” baubles are no accident; Danes have it pretty good and are the masters of invention and reinvention — they have coined everything from Lego to Google Maps. What would be a so-so space anywhere else has a habit of morphing into a fascinating, even fashionable spot over here. Take Copenhagen Harbour, for example, so clean everyone swims in it and so vibrant you can eat at one of the world’s best restaurants alongside it; or northern city Aalborg’s spectacular waterside regeneration from shabby industry to state-of-the-art, attraction-laden leisure area. These people even manage to make sandwiches with no tops — Smorrebrod — into a national delicacy.

For the visitor, this is probably Europe’s easiest destination to enjoy. Yes, its small size aids getting about, but Denmark has had a giant’s mentality for at least a millennium and thus a large country’s diversity of sights in a much more concentrated space, so you will seldom travel even a few kilometres without encountering a tantalising distraction. Its culturally thrumming towns and cities boast pristinely preserved medieval architecture and world-class museums, and some of northern Europe’s most delightful swathes of sandy beaches are close by. But in the main, a trip just glides along with the pleasurable effortlessness of a clean, green, well-oiled machine: cycle paths are superb, public transport works wonderfully, English is well and widely spoken. Oh, and you will eat and drink fantastically, and not just because of the many Michelin-starred heavy-hitters: Denmark vies with the planet’s best in the spheres of butter, bacon, beer, coffee and pastries, not to mention those ubiquitous semi-sandwiches.

For the visitor, this is probably Europe’s easiest destination to enjoy

Travelling in Denmark, you quickly learn to expect the unexpected and even the unprecedented: the place inspired Hans Christian Andersen’s fairytales, after all. Squeezed between the rest of Scandinavia and continental Europe, it stands out from both landmasses with nation-defining traits such as its much-loved royal family, its rejection of the euro and its universally embraced concept of hygge, entailing finding wellbeing through cosiness and delight in life’s simple, immediate things. Whether you seek serendipity or good old-fashioned happiness on a holiday, this is a fine place to start.

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Main photo: Kronborg Castle in Helsingor (Alamy)

Start with the capital. Lap up leviathan art galleries such as Statens Museum for Kunst, ogle at the ostentatious palace of Amalienborg, residence of the Danish royal family and have fun — how could you not? — at the world’s oldest and second-oldest amusement parks, Bakken and Tivoli Gardens. With city sights seen, your urge will likely be to beeline west towards Funen and Jutland, but reserve time beforehand for exploring Zealand, the island on which Copenhagen sits. Linger at fantastical fortresses Frederiksborg (the stately one) or Kronborg (the moodier one that Shakespeare’s Hamlet called home) or stop by Roskilde for its cathedral and compelling insights into Viking heritage.

The next stop for those with limited time but boundless ambition is Odense, Funen island’s largest city. Its maze of gaily painted, timber-framed medieval buildings supply the fairytale-like environs in which Hans Christian Andersen spent his childhood. The main tourist route then swings north up the east coast of Jutland, the only Danish part of mainland Europe. The cities of Aarhus and Aalborg each exude their own vitality, melding Middle Age charm and sleek modernity, and are loveable enough to use as bases for forays into the countryside beyond.

Further north is Skagen, an otherworldly spot to which artists began flocking for the striking light and peaceful rural character 150 years back. The surrounding spellbinding forests, huge dunes and stunning beaches taper out at nearby Grenen. This is the nation’s northernmost tip and one of a few places on Earth to see two seas, in this case the Kattegat and Skagerrak, collide: a poignant point to contemplate Denmark’s far-flung outposts further towards the Arctic: the Faroe Islands and Greenland.

The cities of Aarhus and Aalborg each exude their own vitality, melding Middle Age charm and sleek modernity

Palatial, centuries-old hotels; trendy boutiques: Copenhagen’s accommodation has it all, and across a wide choice of neighbourhoods from ornate, medieval Indre By, the inner city, through to the likes of edgier, multicultural Norrebro. Stay put in Copenhagen for all Zealand sojourns; Odense and Aarhus deliver the best stays among the smaller Danish cities. Denmark is fringed with fine white-sand strands, but top picks for beach stays are the Skagen area, the seaboard along Thy National Park and balmy Bornholm off the southeast coast. The Danish countryside has its own distinctive brand of accommodation, the kro — these former royal staging posts now often offer upmarket stays akin to well-to-do rural inns.

Despite — or perhaps because of — proximity to Copenhagen, much of Zealand and the islands on the key transport artery from northern Germany to the capital, Lolland and Falster, go unexplored. On Zealand try Hornbaek for beach downtime, Gilleleje for scrumptious off-the-radar seafood or a sojourn in handsome medieval Koge. Lolland’s excellent Middelaldercentret (Middle Ages Centre) open-air museum near Nykobing Falster, or a ramble along the mighty wooded chalk cliffs of Mons Klint (Mon), are also fine detours.

Odense steals the limelight on Funen but the most winsome countryside is down on grassy, sandy South Funen Archipelago, a collection of 50-something teensy isles you can hop between. Over on Jutland, dip down to Ribe, Scandinavia’s oldest town, by which point you are virtually on a west coast bejewelled by Denmark’s two loveliest national parks. One of Europe’s most important wetlands makes up Wadden Sea National Park, while Thy National Park protects a wind-pummelled tract of top-drawer Danish coastal scenery: titanic sandy beaches and dunes enfolding Scandinavia’s foremost surfing spot, Kitmoller, dune heathlands and conifer forests that despairing locals planted two centuries back to rein in the shifting sands. Select Silkeborg for an overnight in Sohojlandet, the lake-splashed region spanning much of inland northern Jutland.

May to August is best for enjoying the most clement weather, the most blooming countryside and the majority of the festivals; April and September can still be good for outdoor activities, but outside these months most accommodation and attractions close in smaller places and sticking to city sightseeing is wise.

Is Denmark expensive?
Denmark drains your holiday funds fast. After London and the Swiss trio of Geneva, Lausanne and Zurich, Copenhagen has Europe’s highest cost of living — and this includes accommodation and eating out. Big city chains such as Cabinn offer the cheapest decent hotel rooms with starting prices about £70 for a small single/double.

What is Denmark famous for?
The list is as long as it is diverse. Just a few include: Hans Christian Andersen’s fairytales, Lego (and Legoland), cutting-edge design, Nordic noir, new Nordic cuisine (Noma et al), Carlsberg, butter, Danish pastries, that salty, weirdly addictive liquorice, Lars von Trier films and cycling absolutely everywhere.

Is Denmark safe at night?
As the writer Sybille Bedford once described Denmark: “…enjoyment without anxiety, compunction, heartache . . . the water is safe and the wallet is inside the pocket”. Some care should be taken in certain Copenhagen neighbourhoods such as Vesterbro and Norrebro, but by most European or North American big-city standards even these areas are pretty safe.

Currency krone

Take me there

Inspired to visit Denmark but yet to book your trip? Here are the best packages from Tui and Jet2 Holidays.