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Art, architecture and hipster cafes in romantic Jeju

The popular South Korean holiday island boasts stunning museums and scenic vistas

Jeju is made for romance. It even dots the "j" in its name with a heart, in its official tourism logo.

Scores of K-drama serials have been filmed on the beloved South Korean holiday island and honeymooners flock to its stylish (and expensive) rental cottages that seem to have come straight out of a Scandinavian design magazine.

So what are two women like me and my friend, Park So Young, doing, puttering around Jeju-do in a lilac-hued Chevrolet Spark?

We channel Thelma and Louise - minus the crime and car chases. Motoring anti-clockwise around the rugby ball-shaped island, we eschew the usual tourist spots in favour of art, architecture and hipster cafes. Jeju has these in spades.

But, really, there is no avoiding romance in Jeju.

DAY 1

Drive to the airport, pumping our fists in the air.

A domestic flight from Wonju Airport to Jeju on Korean Air costs about 140,000 won (S$163) and takes less than an hour. The airport utilises a military air field, so security is tight (no photos) - but men in uniform salute you when you trundle to the tarmac on a shuttle bus.

From my seat on the plane, I can see servicemen scrubbing floors in the distance while fighter jets and helicopters take off. Tired, the men sit on their pails and gaze into the distance. Cue Descendants Of The Sun fantasies.

Once in Jeju, we head in our small car towards Aewol, a sleepy harbour town about 8km from the airport. We ooh and aah at the pretty views of rocky black shores and blue waters along the shore road.

After checking in at the Villa de Aewol (www.villadeaewol.co.kr), a boutique hotel with big rooms, good water pressure and reasonable rates, we head to Go Nae for octopus noodles.

The three-year-old restaurant we end up in is run by Mr Lee Yong Seop and his wife, originally from Wonju. Their noodle broth is peppery, with just the right amount of spicy kick, and the sliced octopus is fresh and springy. The free flow of pickled onions accompanying the noodles (8,000 won) are delicious and add a tangy dimension to the dish.

Having worked in real estate in Shanghai, Mr Lee can speak Mandarin and we talk about the rapid changes in Jeju: their cute restaurant, decorated with knick- knacks and featuring cosy window seats, used to have a sea view.

Sadly, the view is now marred by a multi-storeyed building coming up right in front.

Still, Go Nae is a pleasant little village. Anglers stand on the little pier with their long rods, waiting patiently as the fog slowly rolls in.

At a roadside shack called Rich Mango, families and young couples drink mango smoothies at picnic tables while checking out the Siberian huskies penned in the backyard.

Further west, down the coast, we join the Bigbang fans at Monsant Cafe (2546 Aewol-ri, Aewol-eup, Jeju-si), which is said to be owned by the K-pop group's flamboyant member, G-Dragon.

The pretty stretch of coast here already boasts Bomnal Cafe with its twee swings and benches, perfect for romantic canoodling. But Monsant has upstaged Bomnal, with its chic factor: Designed by Korean architecture studio Platform_a, it is a mirrored house with basalt rock and crushed concrete walls, perched on rocky headland.

Take your artisanal coffee and designer cakes alfresco and you will be burnished by the wind, with magnificent views all around. We stay until after sunset, then drive back while the ships light up like stars on the horizon. It is easy to see how Aewol, which literally means "cliff moon", earned its poetic name.

DAY 2

In the morning, we grab a coffee from Indigo dessert cafe (204 Aewol-eup, Aewolhaean-ro, Jeju-si), then pick up takeaway churros and burgers from Jeju's famed Monster Salon (1669-1 Gwakji-ri, Aewol-eup, Jeju-si).

Suitably provisioned, we then set off for Seogwipo, Jeju's second largest city after Jeju-si (or Jeju City). The route winds through mist-shrouded forests and hills.

Along the way, we stop at Bonte Museum (www.bontemuseum.com), designed by Japanese architect Tadao Ando and featuring his trademark concrete walls.

The private museum, named after the natural state of things, houses a modest collection of traditional and contemporary art.

There is a separate building devoted to Japanese artist Yayoi Kusama's works, including the addictive Infinity Mirrored Room - Gleaming Lights Of The Souls, which is filled with 100 colour- changing lightbulbs. Standing in it is like standing in a galaxy of stars or amid winking Christmas decorations. Magical.

A whistle-stop is in order at Bangju Church (427 Sangcheon-ri, Andeok-myeon, Seogwipo), designed by Korean-Japanese architect Jun Itami. Completed in 2009, the church is shaped like Noah's Ark. On brilliant days, its roof of geometric tiles sparkles.

At nearby Camellia Hill (www.camelliahill.co.kr), touted as the biggest arboretum in Asia at about 200,000 sq m, we settle by a water lily-filled lake to eat our Monster burgers. The burgers are juicy and delicious, despite having spent hours in our car before we eat them.

Camellia Hill, too, is pretty, with Instagram-able spots aplenty. There is a forest path strung with lights, a greenhouse filled with - what else? - camellias, and huge lawns with bean bags and dog-shaped seats for kids to romp in.

It is evening by the time we roll into Seogwipo. Our hotel M-Stay (www.mstayjeju.co.kr) is a stone's throw from the Maeil Olle Market. We buy boxes of omegi-ddeok, a Jeju traditional red bean paste-filled rice cake dessert, and orange-, green tea- and cactus- flavoured chocolate (about 10,000 won for eight boxes).

DAY 3

Part of Jeju's romance stems from the role it has played in inspiring Korean artists through the ages.

The most famous of these artists, arguably, is painter Lee Jung Seob, whose bull paintings symbolised Korea under Japanese colonial oppression. Lee spent a couple of happy years in Seogwipo, living with his Japanese wife and two sons in a room measuring just 1.5 by 2.4 m.

The thatched cottage the room is in still stands - a 10-minute walk from our hotel.

We visit the cottage, with its simple memorial to Lee within (the rest of the cottage is inhabited by a Jeju family). The street in front of the cottage, where he used to take his walks, was renamed Lee Jung Seob Street in 1996 and boasts an art market on weekends.

There is also a Lee Jung Seob Art Museum up the hill, where some of Lee's slightly Fauvist works from his Seogwipo period are on display.

Child-like joy is evident in these 1950s works such as Family, painted on the silver foil of cigarette boxes because of shortage of art materials during the Korean War: Lee's naive-looking mother, father and child figures tumble gleefully in space, capturing the hurly-burly of young parenthood.

Lee would be separated from his family, after his wife returned to Japan with their children, and die alone and penniless in 1956, at the age of 40.

So Young, with her musician's soul, is taken by the optimism in Lee's early work. We also decide that the late artist is handsome - like a character straight out of a Wong Kar Wai movie, especially in the iconic black-and-white photograph of him lighting a cigarette.

Buoyed on this lyricism, we head to Seopjikoji, an area writers, artists, scholars and monks visited to meditate. These days, a luxury resort development named Phoenix Island (www.phoenixisland.co.kr) has been built on the site, featuring two more Tadao Ando buildings.

The Glass House has a Zippo Museum and a restaurant, Mint, while Genius Loci is a meditation centre.

We pay the 4,000 won admission fee for Genius Loci, where concrete forms frame the surrounding landscape: a rectangle cut out in a stone wall results in a kind of scroll painting of nature - yellow rapeseed flowers, horses grazing and a majestic tuff cone in the distance.

Keep walking and you end up underground, where four galleries house different video projections - of a tree slowly losing and gaining its leaves, for example. Walking through the Genius Loci is a quiet, spiritual experience. Trade your shoes for room slippers as you enter each gallery.

The path you can take circles a square room that you can see into, but not enter until the end. Such repetition and surprise evokes a Buddhist element of reincarnation and enlightenment. It also strikes me as a little like being in a game of Monument Valley.

While So Young devours what she would later tell me is a pricey but extremely good bowl of champong seafood noodles (about 25,000 won) at Mint, I explore the Seopjikoji bluff, which features dramatic views from a lighthouse as well as azure waters lapping at geological formations.

Then it is off to Seongsan Ilchulbong, or Sunrise Peak, the tuff cone spied from Genius Loci. A Unesco World Heritage site, Seongsan Ilchulbong was formed about 5,000 years ago, when a volcano erupted on a shallow seabed.

At 180m above sea level and with a crater 600m across, the tuff cone used to be an island, until soil erosion formed a narrow strip that joined it to the main Jeju island.

Seen from the air, it resembles a giant green pimple; a crown with its jagged edges. Hiking up to the top takes about 30 minutes and we spend an hour there looking at white boats sailing past the edges of the crater and sniggering at the travellers taking a million photos.

At 1.30 and 3pm daily, Korean "mermaids" can be seen at the base of the tuff cone. Haenyo, as these female divers are called, take the plunge using a special breathing technique that allows them to hold their breath for more than three minutes.

Many are in their 70s, as their numbers decrease. At Seongsan Ilchulbong, they sell fresh seafood from their daily catch to tourists at 10,000 won a pop. I ask for an empty shell for a souvenir instead and a haenyo gives it to me for free.

Dinner is at an accidental find (So Young keyed in the wrong address into the GPS): Seongsan Huay Kuan (8 Seongsan-jungang-ro, Seongsan- eup) is a former fishermen's gambling den transformed into a restaurant by Seoul transplants Sarah Park and her husband, Jae Kim. Opened in September last year, it has since become a cult favourite with young Korean travellers.

We have the abalone rice (15,000 won) that comes au gratin in a hot pan, shaped like Seongsan Ilchulbong.

Then, we settle in with beer and yuzu tea, in the comfortable living room-like space, full of vintage furniture and lace drapery. The couple at the next table are having a fight and giving each other the cold shoulder. Which is a shame, really, because - on this serene, star-lit night; in this low-sprawl fishing town - Jeju is for lovers.

DAY 4

I climb Seongsan Ilchulbong again, at 5.30am, to beat the tourist hordes and see the sun rise over its Eastern rim. Unfortunately, it is a misty morning and the sunrise is nothing but a diffused lightening of the heavens. Sitting on the platform for an hour, I soak up the atmosphere. As I make my descent, the early-bird tourists are already doing their thing: puncturing the morning hush with the electronically induced clicking of digital shutters.

Driving back to the airport, to catch our plane back to Wonju, I want to do a Thelma at The Grand Canyon and tell So Young that "I feel wide awake".

But tuff cone-climbing at sunrise has taken its toll and, as So Young guns the little Chevy Spark down the highway, I fall asleep to the sounds of Korean pop singer Park Sung Shin crooning wistfully for "one last chance".

•Clara Chow is a writer in residence at Toji Cultural Centre in Wonju.

A version of this article appeared in the print edition of The Sunday Times on June 26, 2016, with the headline 'Art, coffee and views in Jeju'. Print Edition | Subscribe