Begin your ride at Frederiksberg Gardens, the romantic estate of former king Frederik VI. Within its gates are twisting canals and elaborate bridges, expansive lawns, a wild zoo, and the royal palace towering over the menagerie below. Pause to explore the sprawling gardens on a boat tour, the original way Frederik would entertain his guests.
Pedal over to Jaegersborggade, a buzzing street located in the satellite neighborhood of Norrebro that's earned a reputation for being one of the hippest blocks in the entire city. The short road boasts more than 40 shops, including a ceramicist's atelier, a boutique caramel factory, a Michelin-starred restaurant, and a porridge bar (yes, porridge). With youthful, creative energy, it's a little slice of Brooklyn's Bushwick.
The end of Jaegersborggade opens onto Assistens Kirkegaard, a large cemetery where dozens of famous Danes are buried, including fairy-tale writer Hans Christian Andersen and philosopher Soren Kierkegaard. If you aren't keen on touring the gravestones, the park offers one of Norrebro's greenest oases--perfect for a stroll.
Copenhagen commuters; Designmuseum Danmark
Next, zip over the canal toward the city center to find Torvehallerne, described as a "super market," not a "supermarket." This enormous food hall features more than 60 vendors selling everything from fresh fish, meat, and produce to gourmet spices and artisanal chocolates. Or you can peruse the ready-mades if you're hungry for lunch--whether it's Spanish tapas or sushi--and grab an espresso to go at The Coffee Collective to keep your day moving.
Just a block away, Botanisk Have, the city's beautiful botanical garden, covers 25 acres of land with more than 13,000 species of flora sheltered in 27 historic greenhouses. Founded in 1600, and moved twice before settling in its current spot almost 150 years ago, the collection now straddles the old city ramparts.
When you cycle east toward the water, you'll find the exquisite Designmuseum Danmark, showcasing the talents of Danish artists and industrial designers, and narrating the advent of the Scandi-sleek style loved worldwide. The permanent collection even includes an annotated history of the chair, set inside an exhibition space resembling 2001: A Space Odyssey.
Travel a few blocks south to find the Copenhagen seen on postcards: Nyhavn is a dockside lineup of posh, pastel buildings fronted by passing sailboats. Once a busy commercial port, the pedestrian street is now packed with restaurants, live music, and Instagramming tourists.
Across the river is Copenhagen's bohemian 'hood, Freetown Christiania. Founded in 1971 by a group of hippies squatting in abandoned military barracks, the 84-acre area exists independent of the Danish government, and offers a haven for artists with workshops, organic eateries, and marijuana dealing. The society within a society is also rich in real estate, with a stunning lake surrounded by woodland.
As evening approaches, head back across the water. You'll want to set aside several hours for the fantastical world of Tivoli. The second-oldest amusement park in the world (after Bakken, also located in Denmark), Tivoli is less like a contemporary Six Flags than a dreamy combination of Disney World, Lewis Carroll's Wonderland, and a quirky resort. Within its storybook walls are adrenaline-crushing roller coasters, a world-class restaurant, an oddly oriental concert venue, and Nimb, a stunning, Aladdin-esque hotel.
When you've had your fill of thrills, close out the day a few blocks beyond in Vesterbro's buzzing Meatpacking District--an area teeming with trendy bars and restaurants frequented by Copenhagen's young creative crowd. Park your bike and refuel at WarPigs, a pub with its own on-site brewery that pumps out 22 different beers on tap.And if you're missing home, try its authentic Texas barbecue--served in the open-faced smorrebrod style, of course.