Australia was a late addition to our itinerary; a quick stay of just under a week, sandwiched between New Zealand and Bali. How could we possibly see this part of the world without stopping off for at least a few days? With the notable exception of Bill Bryson’s “Sunburnt Country”—a book that will scare the bejesus out of any tourist with its encyclopedic recital of poisonous creatures that roam the land just waiting to bite and kill visitors—we're embarrassed at how little we knew about Australia when we arrived.

The name alone conjured up images of Down Under designed and perpetuated by the country's tourism board since the 1980s: Paul Hogan standing in a bar, tipping his dusty hat and winking, as he sips a cold Foster's lager. Outside, a kangaroo bounds in slow-motion, as a baby joey sticks its head outside mum's pouch. Meanwhile, a koala dozes in his eucalyptus tree, while an Aboriginal man with white stripes and dots painted on his skin nods knowingly while playing occasional bursts of the didgeridoo.

This fiction was shattered when we stepped outside Sydney airport, into a waiting Uber car. As the young Chinese driver whisked us through the streets of the city, we stared at a full-blown metropolis that reminded us of Miami—all gleaming glass tower blocks by the waterfront. As we explored the city during the next couple of days, we decided that Sydney is (visually) a cross between Miami and New Orleans, but run by laid-back California-types.

The architecture is striking: whether you're standing on the steps of Jørn Utzon's Opera House or wandering the streets of Darlinghurst, you can't help but feel that you are in a city with its own pace and identity. Yes, it may have been settled by British convicts and guards—as beautifully documented in The Rocks district by the harbor—but Sydney today is a wonderful hybrid all its own. The residents are young, diverse and cool. Above all else, they are physically fit.

During our first visit to the Royal Botanic Gardens, we were struck by the vast numbers of runners zipping around us. It soon became a running joke (no pun intended) that this was the Australian mating ritual. Packs of young men and women ran in groups, jogging or sprinting, all around the park. We never take anything for granted, so Jona even checked with a local to see if these runners might be training for an upcoming marathon. The young lady sighed and proceeded to unload about all the people still stampeding around us. Apparently, this is what happens every day in Sydney. These young, beautiful human specimens take over the park all day, even though they're not supposed to anymore. I guess they just love running.

Thankfully, there is a healthy coffee and restaurant scene in Sydney as well. We spent three days walking (and walking, and walking) around the city, eating our way through the Asian food trail. By this time, we'd had our fill of pies in New Zealand and were clearly hankering for spices. We were also craving culture, having spent two weeks in a campervan. We must have visited every museum we passed. The most noteworthy was undoubtedly the Art Gallery of New South Wales, which exhibited works by Aboriginal, as well as modern and amateur artists. The renovated building alone was worth the (free) visit.

Towards the end of our stay, we had a magical moment at the Sydney Opera House. While on a guided tour, we stopped in the main concert hall, where the symphony orchestra was practicing for an upcoming screening of “Amadeus.” For a few minutes, we stood in the darkened room, in absolute silence, as the music of Mozart rang around us. The interior of the building is as fascinating as its famous exterior, standing as a testament to the vision of its architect who never saw the completed project. Today, it stands as an icon at the mouth of the harbor, the most recognizable emblem of Sydney.

Any decent photograph of the Opera House will also capture the Sydney Harbour Bridge, another landmark construction that frames the water surrounding the city. As crazy thrill-seeking tourists climbed the bridge above us, we took in the sights on foot. We also rode a ferry across the harbor to Milsons Point—the gateway to residential North Sydney—and the delightfully wacky Luna Park, the entrance of which is visible across the harbor.

All of these explorations were made infinitely easier by Sydney's excellent public transport system. The buses, trains and ferries are all cheap and dependable, using a charge card called Opal, which can be topped up as you go.

We stayed in a small Airbnb apartment in King's Cross, which used to be the red light district, but is now, to the dismay of locals, only slightly decadent and could even be described as hip. It's the kind of place where you can get lost in alleyways, cresting a hill, only to find yourself in a completely different neighborhood. However, it’s hard to get too lost, because most roads lead to the water or provide peekaboo views of distinctive landmarks. It hard to convey the sense of wonder at stumbling upon prehistoric-looking ibis birds or exotic cockatoos grazing in a park, while everyday urban life rolls on by in the background. It’s easy to feel like a gawking tourist here. Sydney is a city with character that is worthy of patient exploration and discovery.

After only four days, we had to move on, as we were planning to drive out to a wildlife sanctuary in the Central Coast, northeast of the city. While the sanctuary was well worth the visit, allowing us to get up close and personal with a sweet koala named GumNut and dozens of kangaroos, we soon regretted our decision to leave the city.

The suburbs of Sydney were nowhere near as young, diverse or fun. To push the Miami analogy further, Sydney is also cosmopolitan, while its surrounding regions feel more like the “Deep South,” where visitors aren’t too welcome. The main action was in the malls. We could have been anywhere really. We tried to see the coastline and find unique locales, but very little was geared towards outsiders. We'll leave our hair-raising tales of driving for another day, because they could fill a whole separate article. Suffice it to say, stick to public transportation and the city!

On our way to the airport, we had to drive back through Sydney and were filled with awe all over again. We saw the Opera House and Bridge from a distance, beckoning for another date, winking at us from the blue, twinkling harbor. We were smitten. Don't worry, Sydney: we'll be back.