We had been walking through Seoul for hours in the thick July heat. At least it wasn’t raining. More than one travel Web site had warned: Avoid South Korea in July. Rainy season.

But rain hadn’t materialized. Instead, it was hot and sunny, in a smoggy way, as we searched for one of three World Heritage sites mentioned in every tourism description of the city. We’d gotten lost. Now we were off the main roads, wandering through one of the few Seoul neighborhoods to retain an unsullied array of traditional one-story wood buildings topped with the dramatically arcing barrel-tile roofs, which instantly said “exotic East.” We turned right, then left, then right, wandering through mazelike alleys, until we noticed a man gesturing from a block away.

I thought maybe he was waving to someone behind us, but ... nobody there. The man gestured again, a big sweep of his arm. Was he upset we’d invaded the residential area and telling us to get out? Or was he beckoning us deeper into the maze?

Then I saw what he was pointing us toward: Barely visible in the narrow space between tightly packed eaves was the peak of a magnificent rainbow-hued building with the unmissable backward swastika that denoted a Buddhist temple. He’d just wanted to make sure we didn’t walk past without seeing it.

Now that we were heeding him, he led us down another alley to an entrance gate topped by a pagoda out of some psychedelic fantasy, its intricately carved eaves bursting with neon-painted lotus blossoms and engraved scenes from the life of the Buddha. The man wandered off without a word.

The main entrance of South Korea’s Songgwangsa Temple in Suncheon. The temple was founded in the 9th century and is considered an important place of worship in the country. (Shin Woong-jae/For The Washington Post)

“You won’t find the cities beautiful, like in Europe,” warned our son, Sam, nine months into a year of teaching English in a provincial Korean city. “But there’s this different kind of beauty here. You might not see it. It took me a while.”

We had 10 days.

My wife, Lisa, and I had both wanted to do more traveling now that our kids were out on their own, but South Korea would never have made our top 10 list, or even top 20. In that, we were no different from most. If Americans make the exhausting, disorienting trek to East Asia, they go to China and Thailand mostly. Not that Korean tourism wasn’t experiencing a boomlet — 12 million foreign visitors in 2013 — but the vast majority were other Asians, Chinese mostly, lured by the export of a faddish “Korean wave” of unbearably cutesy teen pop music groups, TV soaps with uniformly gorgeous stars and the plastic surgeons who had made those stars so good-looking in the first place. (A plastic surgery vacation is not my idea of good fun, but apparently 50,000 Chinese with yuan burning holes in their cellulite disagree.)

That July, 400,000 Asian tourists visited South Korea, but only 35,000 Americans. By contrast, almost 50 times as many Americans would go to Europe that month.

When we watched a documentary on the tragic 1950s American military intervention in Korea as a way of getting historical background, we noticed with amusement that the announcers in the creaky newsreel footage kept calling Korea “this virtually unknown country.”

That’s no longer true, of course — not with Samsung, Hyundai and LG in every home/garage/pocket — but those consumer goods did not come with a mental image of Korea as an appealing travel destination attached.

Even so, we wanted to see Sam and share in his excitement about living abroad. As we went online to book flights (expensive and interminable) and hotels (good ones are notoriously sparse and hard to locate on English-language Web sites), we plunged forward with more grim determination than giddy anticipation.

A cable car descends from the top of Seoul’s Namsan mountain. (Shin Woong-jae/For The Washington Post)

We emerged from the exhausting odyssey halfway around the globe into a steady rain outside of Seoul’s towering modern central train station. The cabdriver couldn’t make any sense of the Roman lettering on the map I showed him, or, apparently, the Korean script written beneath it. We drove around, seemingly randomly, for half an hour as I contemplated the hopelessness of our jet-lagged situation. It was only by chance that, scouring the map, I noticed a small-print number of 11 digits at the bottom, which thankfully the cabbie recognized as a phone number — the hotel’s.

Our room, barely bigger than the beds it contained, was otherwise pleasant enough, with all the modern conveniences you’d expect in a middle-rung American hotel. To us, at least in that moment of pure exhaustion, the perfectly comfortable beds were nirvana.

We’d barely woken in the morning when my phone emitted an odd chime. This was my son calling on a free app called KakaoTalk, which allowed us to call each other without paying the ruinous Verizon international call or roaming charges, as long as we had WiFi, which fortunately seemed to be everywhere . We were already beginning to discover the duality of Korea: still a developing country in some ways — the congestion, the raw, somewhat slapdash construction that made everything seem grimy, and the chaotic city planning — but way ahead of the United States in others, like a subway system that in size, convenience, aesthetics and low cost made Metro seem like a series of high-priced donkey carts. Also: a bullet train system that reached every significant city in the Kentucky-size country in an affordable, and quite comfortable, few hours.

Now that Sam, a whiz at languages who’d become quite conversant in Korean in less than a year, was with us we didn’t have to sweat the communication gaps. We set off walking in the monstrous megalopolis of 25.6 million — the second largest in the developed world. A cool morning breeze vanished well before noon, followed by heat that rose around us in a molten flood. The smoggy air felt like a solid substance we had to push through as we marched along the uneven, slanting sidewalks.

Seoul sits in a bowl, split by the Han River and surrounded by dramatic rocky mountains.

The steep grade of its streets rivals San Francisco, but any comparisons with American cities are inherently misleading. San Francisco is a tiny village compared with Seoul, and its cityscape easily describable. Seoul is an overgrown mishmash, a frantic uprising of glass, concrete, wood and stone, all thrusting out of the earth like an architectural rapture. Six-hundred-year-old palaces sit at the foot of billion-dollar corporate towers out of a sci-fi fantasy, glittering above neighborhoods of dingy concrete apartment blocks interspersed randomly with traditional tile-roofed pagodas and garish shop fronts buried under an avalanche of signage — from elaborate creations of blinking neon to hand-lettered placards bolted, nailed, pasted or draped over every surface. Streets bend and twist into narrow passages winding through hidden neighborhoods exploding with street markets where vendors hawk everything from high-end electronics to stacks of dried, salted octopus.

We spent three days in Seoul doing the obvious tourist stuff: the impressive centuries-old palace complexes that take up wide swaths of urban real estate, Forbidden City-like; the N Seoul Tower that rises 1,574 feet above the center of the sprawling city, about three times as high as the Washington Monument ; the various serpentine street markets and the arts district of Insadong with its tightly packed shops and restaurants in low-rise buildings covered with flowering vines.

At the end of one long, exhausting trek in the city’s center we came, unexpectedly, to a temple in a kind of doughnut hole carved out of high-rises. On the dirt plaza surrounding the open-sided structure, scores of Koreans in street clothes were kneeling or prostrating themselves on bamboo mats as a monk sitting lotus-style before a massive golden Buddha chanted in a hypnotizing monotone with rising and falling inflections that reminded me, after a while, of the steady advance and retreat of waves breaking on a beach. We found a place to sit on some steps as the chanting continued, falling into a kind of semi-doze. My thoughts rounded like rocks smoothed by the steady stream of sound. At each pause, I expected the chant to end in an out-of-breath huff, but it never did. After 45 minutes, the monk droning on miraculously, we got up and wandered away, feeling as if we had woken from a dream whose wispy remnants clung like cobwebs.

After five days in Seoul we took the fast train to Suncheon, the smallish (by Korean standards) coastal city of 279,000 3 1 / 2 hours to the south where Sam had a tiny apartment among the crowded streets of the “new” downtown. By then, Lisa and I had already begun to overdose on Korean cuisine. We weren’t big meat eaters, and the pork and beef that predominated was lost on us. The bottomless dishes of kimchi and other pickled vegetables that accompanied every meal had begun to overwhelm.

Sam was pained to see his parents cringe at what seemed to us an unrelenting cuisine and flat-out refuse such delicacies as still-writhing octopus tentacles. He seemed especially disappointed that we vetoed a visit to one of Korea’s specialty cafes that featured dogs, or cats, or birds — not on the menu, but alive, wandering around freely as patrons ate and drank. He wanted to visit his favorite of the genre, a snake cafe, the mere mention of which may have scarred his mother for life. He made a sour face when we dragged him to breakfast at a Paris Baguette restaurant — a Western chain! — because we couldn’t stomach a Korean breakfast of rice, soup and those ubiquitous pickled vegetables.

One evening we were wandering around Sam’s neighborhood when we came across an open-air barbecue place with large woks in the center of each table and what appeared to be a live bait tank on the street. The circulating water leapt with shrimp, coursing against the current. The menu choice was either a whole bunch of shrimp or a whole bunch more shrimp. The waiter dipped a net into the tank, pulled it from the water dripping and twitching with crustaceans, then dumped the entire assemblage into the sizzling wok at our table. Those shrimp did violent, flipping somersaults for their lives as the waiter blocked their escape with a glass lid. Only one athletically gifted shrimp managed to hop clear and dove to the concrete floor at our feet, where it continued to flip until the waiter scooped it up in one hand, tilted the lid with the other and tossed that shrimp right back on the fire.

“Now that’s something you don’t see back home,” Lisa said.

Heck, we had to peel them anyway, and the hot sauce and Korean beer washed away whatever remaining sanitation qualms we may have had.

Shoppers search through options, many of them swimming in tanks, at Noryangjin Fish Market. (Shin Woong-jae/For The Washington Post)

The next day we walked down a wide boulevard past the same mind-blowing mix of glitz and funk as Seoul only to emerge on a quiet, shady street leading to a cafe whose wide windows opened to a tree-canopied park. Inside, classical music trickled from the speakers and fine art hung on the walls. We felt like we’d stepped through a portal and emerged in Prague or Paris. In another direction, the boulevard gave way to a twining web of narrow streets that led to a bridge across the river, which looked out on a lushly forested hill rising above the city’s center. We climbed steep switchback stairs through tunnels of bamboo and mature shade trees to the top, where we sat at a small table enjoying a breeze and at least a five-degree drop in temperature while a woman inside a striking pagoda-like structure lovingly arranged a bowl of bingsu — shaved ice, sweetened with condensed milk, topped with sweet red bean paste and garnished with fresh fruit and sugar cookies. It was delicious. In fact, the whole experience was delicious. It felt as if we were floating on a peaceful cloud high above the hot, churning city.

We wandered back down into the heat and boarded a city bus that Sam had discovered. It wound through the outskirts of town, then high into the mountains until it arrived at a large parking area surrounded by open-air restaurants. From there, we climbed a steep path through the woods alongside a tumbling mountain stream that from time to time broke into impressive waterfalls. The path rose, then crossed the stream on an ancient bridge made of moss-covered stones to a two-story pagoda beside the rushing white water. The half-dozen structures of the Seonamsa Buddhist temple emerged just beyond, surrounded by stone walls and constructed of whole timber carved and painted in astounding detail beneath the arcing tile roofs, set in relief by the mountain peaks beyond. There had been a temple here for 1,200 years, ever since Buddhists were pushed out of Korea’s cities into remote mountain retreats like this one.

The main path led left, but we cut right, up a grade so steep I had to lean forward to stay upright. At the top was a series of worn granite steps leading to another complex of buildings. We were invited inside by a woman who offered, for a minimal fee, to serve us green tea and cookies on low tables in a wood-floored room open on three sides to the surrounding mountains.

We had the place to ourselves, and we lingered for as long as seemed polite, sitting and staring out at the temple courtyard and the mountains beyond. In the main temple complex down the hill, a few tourists (though no other Westerners) wandered the plazas as novices in brown robes and monks in white robes prayed and chanted, or went about their chores.

Behind the temple complex, a path soon became a steep, rocky climb through a breathtaking stand of tall cedars to the summit, and then down to another equally spectacular temple called Songgwangsa. We’d reached the end of our hike-ability, but Sam had frequently made the four-hour trek with friends and discovered spectacular waterfalls carving out rock swimming holes in the mountainside, not to mention a 150-foot water slide that plunged down to a precipice and sent bathers flying into a deep pool.

As we descended, we could see the bus, which comes only once an hour, at the far end of the parking area, about to pull out. Sam sprinted ahead and begged the driver to wait for us. He did but was clearly unhappy about it, overcharging me when I caught up, out of breath. It was the only time in our 10-day trip that any Korean was less than friendly or helpful. Irritation surcharge: $1.

A monk holds a chanting ceremony in Songgwangsa Temple. (Shin Woong-jae/For The Washington Post)

We returned to Seoul and spent our final day strolling the ritzy Gangnam district, made famous by that ridiculous viral song , only to realize it was exactly like being in midtown Manhattan, with even-more expensive Starbucks shops. We toured one more World Heritage site — the royal tombs — which were impressive, if you like huge mounds covered with grass. We walked in the preheated oven of the Seoul afternoon.

We meant to wander around until we found a likely restaurant, but we’d waited too long and had grown low-blood-sugar cranky. Sam especially was on edge. It made him tense looking for a place, he said, because he knew we hated Korean food. No matter how much we denied it, he remained unconvinced. Predictably, after we’d passed by a dozen potential eateries — “That’s a chain!” Sam said, horrified, of one — we entered a stretch of no possibilities at all.

I didn’t blame Sam. I knew he was anticipating our departure, anxious that maybe we’d been underwhelmed by his adventure. That we hadn’t been able to make the leap, to see Korea through his eyes. The food was just a metaphor.

But you can’t eat literary devices, and we really needed to eat. I felt our situation teeter on the edge of unpleasantness when I looked down a steep alleyway and saw an obscure door just below street level with a sign in English below the one in Korean that said, “Yakitori.”

It wasn’t Korean — and I saw Sam flinch — but at this point, I was willing to impose.

We trouped down the stairs into a long, narrow, cavelike space burrowing into the hill, taken up almost entirely by a gleaming wood bar. We sat at a table in the back, beside a few others filled with young Koreans. The waitress addressed us in perfect American English and explained that their menu consisted of five varieties of yakitori, which is essentially Japanese-style barbecued chicken served on a spit. We consumed every platter and washed it down with refreshing Korean sake, served cold instead of warm, as in Japan.

As we ate and drank, Sam visibly relaxed. We began to talk over all the things we’d seen and done, realizing only as we spoke just how astounding they had been. We paid and spilled back out onto the street. It was as if we were actors in a play, and the scene had changed.

Someone had clamped a rose filter on the sun, and the temperature had dropped at least 10 degrees. We climbed the hill and stood on a bridge over an ancient creekbed. Where water once flowed, a meadow had grown up, studded with wildflowers. On either side, the domino-block apartments tumbled against one another, their unpainted exteriors now bathed in a warm wash of pink. Every balcony, every rooftop blossomed with tall tufting cornstalks, lush herbs and tomato vines bending low with red fruit. The sun hung heavy and ripe itself, just above the mountains to the west.

To the east, the city flared skyward in profusion, a garden not of plants, but of human fancy. Its citizens streamed past along the bridge, striding confidently into what would most certainly be the Asian century.

I saw it. I definitely saw it.

If you go

■ At the Noryangjin fish market in southern Seoul, pick out your meal while it is still swimming in aerated tanks, and it will be netted and prepared on the spot.

■Take the Namsan cable car up Mount Namsan in central Seoul to the N Seoul Tower. From a platform at the foot of the tower, you can get a breathtaking 360-degree view of the city, 800 feet below.

■ Visit the Daehan Dawon Tourist Green Tea Plantation near Boseong, about five hours south of Seoul by train. The winding hedgerows of tea create beautiful patterns as they rise up the steep mountainside with the sea shining in the distance.

Tom Shroder is the former editor of the Magazine. His most recent book is “Acid Test: LSD, Ecstasy, and the Power to Heal.” To comment on this story, e-mail wpmagazine@washpost.com or visit washingtonpost.com/magazine.