July 18, 2014 1:56 p.m. ET  MY LUNGS were burning, my legs wobbling. My first outing as an Olympic athlete was not going well. Then again, I was burdened with a backpack and jet lag.  My 11-year-old daughter had decided that the best way to experience ancient Olympia—a sprawling riverside complex in Greece where the Olympic Games were held starting in the eighth century B.C.—was to run the roughly 200-yard track that Zeus's son Hercules supposedly laid out. Under the scorching midday sun, was it a smart thing to do? No. Did it make antiquity come alive in a rush that I can feel again typing these words? Ye gods, yes.  My daughter, Honor, is not only an athlete but a bookworm—particularly when it comes to Rick Riordan's best-selling Percy Jackson series for kids. Mr. Riordan's books, which follow the fictional children of the Greek gods as they roam the modern-day world, have inspired a wave of adolescent fascination in ancient myths and the characters who populate them. They spurred Honor to explore the subject more deeply—she was surprised to learn that the author didn't create all the mythology in the books, while I was taken aback that he'd placed Mount Olympus atop the Empire State Building. And they prompted me to plan a week-long trip to Greece as an educational adventure.  I hoped to show Honor how Mr. Riordan tapped into some of western civilization's founding stories; what I didn't expect was that she would end up teaching me, too.  Greece is an extraordinary place to visit, perhaps never more so than now. Upgraded museums have transformed how people experience some of the world's most famous sites; fast, modern highways have put much of the country within easier reach; and prices are low. Our goal was to road-trip to as many spots related to the divinities as we could—including Athens, Delphi and Olympia—before greeting the gods en masse at Mount Olympus, Greece's highest mountain and their fabled home. We would then fly to the island of Crete to see where Zeus is said to have lived as an infant.  My daughter dubbed our tiny white rental car Pegasus. Before the trip, I researched scenic drives in Greece, but that turned out to be unnecessary: the windshield was our private IMAX screen, showcasing mile after mile of mountains, coastline and olive groves. We let local drivers careen past while we enjoyed the sights and smells at a leisurely pace (one afternoon, it seemed like every home in the village we were rolling through was sautéing garlic in olive oil). We splurged once or twice on accommodations, but mostly opted for the simplest hotels and were still treated like, well, gods.  Readers of Mr. Riordan's books learn early on that Percy Jackson's dad is Poseidon and that his friend Annabeth is a daughter of Athena. So Honor and I started by chasing down the parents in Athens, a city the two gods famously fought over. According to myth, Athena, goddess of wisdom, and Poseidon, god of the sea, each wanted to claim the metropolis as their own and competed to impress the citizenry. Atop the rocky hill now known as the Acropolis, Poseidon called forth water from the ground, but his spring was salty. Athena's gift was more useful: an olive tree. Grateful Greeks built (and rebuilt) temples to honor her, including the now nearly 2,500-year-old Parthenon.  My daughter and I were more appreciative of the Acropolis Museum at the foot of the hill. Though stunning, the sun-scoured Acropolis itself was packed with construction equipment and crowds. The cool, calm museum houses most of the site's true treasures, including some friezes that once wrapped around the Parthenon just beneath its roof, now helpfully hung at eye-height. Youth-oriented materials from the information desk allowed us to survey the whole pantheon of Greek gods and preview the rest of our trip: Here was a frieze featuring Apollo, whose temple we'd visit in Delphi; there was another depicting his son Asclepius. We'd go see his sanctuary in Epidaurus.  That afternoon, we drove an hour along the coast to Cape Sounion, a treeless promontory towering almost 200 feet above the Aegean Sea. Around 440 B.C., Poseidon's worshipers built a temple there that, while smaller than Athena's Parthenon, may have the better view: a full 360 degrees, mostly of glittering water. Just beneath Sounion's peak my daughter stopped to brief me on Hecate, the goddess of crossroads. "Two trails, do the math," she said and chose one before calling back: "You coming?" We hiked down the thyme-scented hillside to the quiet, modernist beachfront Aegeon Beach Hotel. After a day in Greece, Honor's verdict on the trip was already in: "This is amazing."  It was a word we'd wear out. The next day, three hours west, we tested the eerie acoustics of the famed amphitheater at Epidaurus, whose construction began in the fourth century B.C. Even a shy 11-year-old's speaking voice can reach the most distant of its 14,000-odd limestone seats. Honor heard lesser figures from the ancient world calling to us, so we wandered through the nearby Asclepieion, a kind of hospital complex from around the same time, dedicated to the healer Asclepios. We visited the basement where "sleeping cures" once took place—dreaming patients were monitored by priests and a slithering squadron of snakes.  Less than an hour away, the expansive, sunbaked city of Corinth boasts a temple to Apollo. Built in the sixth century B.C., it's one of the oldest stone temples in Greece and is now but a cluster of columns. We couldn't ignore the craggy butte just beyond. A 10-minute drive took us to the lofty parking lot of the citadel of Acrocorinth, which for centuries protected the city below. We trekked along the citadel's crumbling walls to the summit. The hike brought to mind Corinth's founder, Sisyphus, condemned by Zeus to spend his afterlife pushing a rock up a hill, only to have it roll back down each time. It reminded Honor that we'd been climbing hills since the Acropolis. "Greece is like acro-everything," she said between breaths, and I grinned, pleased at her knowledge of a Greek prefix for "top" or "tip."  After a night in Nafplio, a port city beloved for its narrow, marble-paved streets—and by my daughter for its abundance of gelato shops—we sped 2½ hours west to Olympia, where my running won smiles but no medals. The track, little more than an open field, was actually the least interesting part of the site, which still felt like an Olympic village, with places for athletes and visitors of yore to train, bathe, sleep and worship. Though the early Games were all-male, my daughter was pleased to see that Zeus's wife and sister, Hera, merited a temple on the grounds. Largely in ruins, the temple is still important—it's where the Olympic torch is lighted today.  A few hours' drive took us across the Gulf of Corinth at Patras and into central Greece. We made the precipitous, twisting ascent to ancient Delphi, on the flanks of Mount Parnassus. Because we arrived in late afternoon, we had the site, lighted with gossamer-gold late-day light, all to ourselves. Fittingly, our destination was another temple to the sun's charioteer, Apollo. Only about six stumpy, wind-worn columns remain, but that made it easy to see the view beyond—which seemed to encompass all of Greece. Zeus is said to have dispatched two eagles to find the center of the world; Delphi was where they connected. No argument from us.  Dinner did spark some disagreement. I insisted we diversify beyond pizza; we found a small taverna on the landing of a broad stairway that climbed through town. How small? After we ordered, the waiter scooted to a market next door to shop for our meal. The moussaka—a layered eggplant dish—was exquisite, and could have fed 20 instead of just two.  We needed the calories. Less a single peak than a long, bare, undulating ridge of rock that scrapes the sky, Mount Olympus is regularly climbed by backpackers from all over. But the mountain still presents a challenge—unlike in Mr. Riordan's books, there is no "special elevator to the six hundredth floor." Instead of hiking up from Litochoro, near the mountain's base, we saved ourselves five hours by taking a serpentine, 30-minute drive to the Prionia trailhead. On foot, we gained 3,200 feet in three hours, climbing through a forest of beech and fir. Honor was in awe: She was actually on Mount Olympus. When we spooked a deer and I joked, "There goes Artemis"—the animals are associated with the goddess—it didn't sound funny. Honor took off running, leaving me to fend for myself. We stopped at a stone refuge three hours short of the highest peak, because the last bit of the trail features sheer drops, loose rock and, usually, snow. As we rested, Honor read a book and I watched Zeus draw a veil of clouds across the summit.  But our trip found its heroic conclusion on Crete. We went to see the Minoan palace of Knossos, whose corridors purportedly served as the labyrinth for the part-bull, part-man Minotaur, and gamely followed catwalks and paths over and through the palace's foundations. The ruins were too sunny and open to creep us out.  But our final stop, the Dikteon Cave at Psychro, was a different story. Embedded in a rocky hillside studded with stunted trees, the cave is supposedly where the infant Zeus was nursed, out of sight of his murderous father, Kronos—a key antagonist in the Percy Jackson series—who feared a prophecy that one of his sons would dethrone him. We drove a series of switchbacks into Crete's interior, then hiked (again) up a steep stone path.  I was fleeced of my last two euros by an "attendant" in the parking lot. That wasn't the admission fee, a ticket-taker informed me when we reached the gate: 4 euros, please.  I showed my empty wallet and explained our quest. He shrugged.  "That's OK, dad," my young mythologist said.  The man coughed. "The girl can go in the cave, free. But," he emphasized, "alone." He looked away, unable to bear her wide eyes. An 11-year-old on her own in a 278-foot-deep cave?  We checked the flashlight on her iPod. I pointed out the stairs, the handrail. She gave a little wave and disappeared.  In good time, having wound through the cave's colorfully lighted stalagmites and stalactites to a tiny "lake" at the bottom, Honor re-emerged, pleased, but not half as much as I. The gods had tested her, and she'd passed.  The Minotaur is a monster in Greek mythology that is part bull, part human. A travel article in Saturday's Off Duty section mistakenly called it a one-eyed monster.
The young-adult book series sent a father and daughter searching for the ancient gods—and made for a divine adventure.