They look over their shoulders at their backdrop – not a sweeping landscape or an elegant edifice, but a two-metre high statue of a penis, carved in terrifying detail. Welcome to Jeju-do, South Korea’s honeymoon island and a place where the normally coy Koreans become impish extroverts.

This is an island of superlatives – it’s home to South Korea’s highest mountain, its southernmost point and its most striking scenery. My friend and I start on a literal high, trekking to the peak of Mount Halla, 1,950m above sea level. South Koreans are not half-hearted people; they are fanatical about pretty much everything – including hiking.

So, as we pass white-haired hikers in fluorescent North Face gear, sporting matching visors and go-faster poles, we feel a little underdressed in our trainers, shorts and T-shirts. But as with most Korean hikes, the going is not too tough thanks to a network of well-kept paths, wooden walkways and staircases complete with handrails. 

Still, it’s a pretty gruelling hike for the out-of-practice – a steep 6km uphill trek that is only outdone by the knee-wrenching downhill return leg. The reward for a two-hour session is a startling view of the island below, with the added bonus of a crater lake in the foreground.

Gazing longingly at the lake-topped peak above us, we join our group for a Korean picnic of kimbap – a rice and seaweed snack akin to sushi rolls – before heading back to our rented moped. With the energetic aspect of our trip dealt with, we turn to the more relaxing pursuits the island is best known for.

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Sometimes called the ‘Hawaii of Korea’, beaches are obviously high on the list of Jeju’s must-dos, but even higher is the string of sex-themed attractions scattered around. In among the more family friendly museums, you’ll find salubrious salutes to all things erotic.

At Jeju Loveland, the island’s original sex attraction, 8km from the capital, we pay $8 and enter the all-concealing walls. It’s an erotic art park, featuring everything from giant figures kissing to grassy hillocks capped with outsized nipples. There’s juvenile giggling as visitors weigh up the urge to take comedy photos with the embarrassment of performing X-rated poses in front of strangers.

Having had our fill of giant appendages, graphic monuments and statues inspired by the kama sutra, we head south to Seogwipo. Jeju’s second city, Seogwipo, is not a pretty place, but the Jeongbang Waterfall just out of town makes you instantly forget the neon-framed maze of backstreets.

Crashing 23 metres straight into the East China Sea, it outshines some of Asia’s famed waterfalls and marks the start of a string of natural attractions. Jeju’s south coast features striking rock formations, a trio of worthy waterfalls and the hopping off point for Marado, a tiny island off Jeju’s southern coast. Like many visitors, we brave the vomit-inducing ferry ride to enjoy car-free roads (the only transport here is golf carts), buildings so pristine they seem to belong in a theme park and, of course, Korea’s southern tip, an unassuming spot that we actually miss as we enjoy Marado’s perfectly manicured panorama.

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We follow a full circuit of Jeju, taking in backwater restaurants and cheesy museums, volcanic caves and gobsmacking beaches.

We take time to explore the Museum Of Sex And Health, a combination of phallic statues, an erotic 3D cinema and exhibits so enthralling we hardly even realise information panels are written in a language we cannot read. Jeju never fails to amaze with its vistas, its variation and its unique attractions, yet it’s clear what makes this island special.

Beaches, waterfalls and even volcanoes are attractions easy to find the world over, but how often do you get to post a profile picture of yourself and a group of giggling grannies ogling an enormous penis?