Eco-chic and with a bohemian flair that extends well beyond the borders of Freetown Christiania, Copenhagen is fresh blast of North Sea air, by turns briny and sweet but always well-designed. A quirky compromise between Scandinavian chill and Germanic heartiness, Copenhagen is a cosmopolitan city on a walkable--or more appropriately, bike-able--scale. So rent a bicycle, scope some Danish minimalism, and grab a sausage and a Carlsberg, and do as the locals do. 

If you're only going once, swallow some shame and check out Copenhagen's tourist clichés. The Little Mermaid statue is quintessentially Danish, commissioned by the Carlsberg family to pay tribute to Hans Christian Andersen's fairy tale, and has justly become the symbol of the city. The salt-lashed Langelinie, the pier, park, and promenade the statue calls home, is worth a stroll, both for the outlet shopping and the other scattered monuments to Danish culture and history. Meanwhile, Danes have making themselves dizzy under the lights at Tivoli Gardens since 1843, so you owe it to your inner child to brave a roller coaster and mount a carousel pony. The Stay Flyer, the world's highest carousel-watchtower, provides some of the best views of the city, if it doesn't spin you senseless first. The ride-averse can still find fun in the live music, pantomime theatre, and lush garden oases.

Brush up on some gruesome Nordic history with the Viking Ship Museum in Roskilde Fjord 35 minutes from Copenhagen or hit the 17th century Frederiksborg Palace for a more polished take on the past. The Open Air Museum brings 100 original farmhouses and buildings from across Denmark and the Faeroe Islands to a field on the outskirts of Copenhagen, allowing you to travel through centuries of history and the entire Jutland peninsula and Danish archipelago without getting your feet wet. The Open Air Museum will ground you in the Danish past, but the Tycho Brahe Planetarium will catapult you to the stars--or the jungle--with a star projector and an IMAX theatre. If you're craving a heavy wallop of official grandeur, check out Stotsholmen, where the Parliament rubs elbows with the Royal Library and Royal Danish Arsenal Museum. More fun and streamlined are the Museum of Art and Design and the Danish Design Centre, where Arne Jacobsen's Egg and Ants chairs, Jacob Jensen's Margrethe bowls, and Poul Henigsen's  PH-lamps get enshrined as masterpieces. 

No trip to Copenhagen is complete without a visit to Freetown Christiania, a tumultuous, freewheeling hippie/anarchist enclave where cannabis is sold freely, drug addicts warmly welcomed, all the homes are squats or shanties, and the threat of government infringement and eviction are ever-present. Whether you're coming to gawk or partake, Christiania is unmissable. 

If you like your intoxicants more legal, take a tour at the Carlsberg brewery, or just sip some of the famous green-bottled lager on the Nyhaven, where the 17th century townhouses are crayon-box colourful, the boats are rigged, and the al fresco dining is superb, whatever the season [restaurants supply blankets for diners hearty enough to brave the North Sea winter]. Snagging a hot dog from one of the van or a danish for a patisserie is the cheapest way to eat, but if your tastes run to the extravagant you can book a table at Noma, where the fare is an expensive riff on traditional Nordic cuisine. It's been named the best restaurant in the world three years running, so you'll have to think ahead to secure a seat. 

Copenhagen is compact and navigable but don't be misled. You can master the map in a day and pay home to the city's greats--Vikings, design, Andersen, and Carlsberg--but stay a week, or even a month, and you'll still be turning up treasures. Slip into a jazz slouch at the legendary Jazzhus Montmarte, scope an up and coming design scene at boutiques like Black Noir and Henrik Vibskov, and hang onto to that bicycle. It's the Danish way to get around.