The moment I lean back on the marble slope of the Oslo Opera House, I realize how ridiculous my plan is. I've just had a glass of wine, and an alfresco snooze is in order, but the opera's outdoor space is busier than opening night for The Barber of Seville. Three Lycra-clad runners whiz by so close to me, I could make them jump hurdles just by extending a leg; a young couple, laughing about scoring 100-krone tickets to tonight's performance, sits down within earshot; and a woman wheeling a toddler who's got the lung capacity of a soprano stops to read the newspaper.
A poetic rendering of gleaming ice floes that have crashed into one another, this building is obviously more than just a pretty face. People immediately adopted the Snøhetta-designed opera house after its 2008 opening – not just as a place to see the national opera and ballet companies but also as lunch-date central, an open-air living room and even a jungle gym for high-octane workouts. So much for my nap; Osloites obviously have way more energy than me.
Energy is the operative word. Fuelled by oil and gas discoveries in the late 1960s, Norway has gone from cod-peddling nation to international powerhouse in less than a generation. A chunk of the cash flow is being spent on transforming the capital from sleepy town to cosmopolitan city, with such stunning projects as the opera house. Sidsel Krokstad, a lifelong Oslo resident and my guide for the afternoon, meets me on its marble steps and leads me up to the roof; from this perch, I lose count of the construction cranes. If the opera is a symbol of the city's unpretentious, democratic nature, it's also an emblem of a boom that has given its sports-crazy citizens a designer ski jump in steel, courtesy of Denmark's avant-garde JDS Architects, not to mention the Renzo Piano-designed new home of the Astrup Fearnley Museet, which showcases modern art under a sail-like roof that almost dips into the Oslo Fjord.

The opera house's wood-clad performance hallThe opera house's wood-clad performance hall

Before leaving the opera house, Krokstad ushers me inside, past the glass and marble exterior. "You'd be hard-pressed to spot a single right angle in this building," she says, looking around at the sloped and curved walls. Then she nods toward the massive, semicircular wooden wall that rises like a giant oak tree in the centre, its core comprising the stage and seating for some 1,300 spectators. As I crane my neck to take in the scope of this "trunk," I'm reminded of Yggdrasil, the tree in Norse mythology that connects heaven and earth. And that's when it hits me: The opera house is a metaphor for a nation that's busy creating a new, polished mythology for its 5 million inhabitants.

Aku-Aku Tiki BarGet into a southern spirit at Aku-Aku Tiki Bar, a Grünerløkka fixture that serves 36 types of rum – and a killer mai tai.

I pick up a bike from the Oslo Bysykkel bike-share program and start pedalling along the Akerselva River, in the city's Vulkan district. Before long, I swing by a waterfall and, after ducking under some weeping birch trees, wave hello to a man with a fishing rod. It's hard to believe that only a few years ago, this popular green space – once the cradle of Oslo's industrial revolution – looked like a dump. I cross a bridge and steer into Grünerløkka, a bohemian neighbourhood distinguished by eclectic watering holes and restaurants, including Aku-Aku Tiki Bar, where I join the after-work crowd for a spicy chili rum punch, and Villa Paradiso, which has me lining up for the thin-crust, Napoli-style pizza. The apartment buildings, which used to house workers from the nearby factories, have been spiffed up to show off intricate leaf patterns and geometric shapes set against facades painted aquamarine, ochre yellow and dusty rose, hues more common in the Caribbean than in Norway.