Day 1: Yokohama, Tokyo, Japan

Tokyo is the largest city on earth and packed with some of the world’s best shops, museums and restaurants, big and small. While the bright neon lights and the bustle of contemporary Tokyo may be what comes to mind when you think of the city, there is another side. Tokyo's historic gardens and neighborhoods of traditional homes on narrow lanes speak to a timeless Japan that has survived into the 21st century.

Day 2: Shimizu, Japan

Widely regarded as one of Japan’s most beautiful ports, Shimizu affords peerless views of Mount Fuji on a clear day and claims the scenic Miho-no-Matsubara pine forest as a backdrop (both are UNESCO World Heritage sites). The port’s temperate climate and rich culture—heavily connected to the surrounding Shizuoka region—have made it one of the country’s prime sightseeing destinations. A few of the main attractions include Kunozan Toshogu Shrine, designated a National Treasure by the Japanese government, Sumpu Castle (built in 1586) and Shizuoka Sengen Shrine, where warlord Tokugawa Ieyasu, who ushered in the Edo period, held his coming-of-age ceremony. Tokugawa shoguns ruled Japan for 250 years, until 1867. The broader region offers plenty in the way of picturesque coastal landscapes, tea plantations and a wealth of Buddhist temples and Shinto shrines, while the port itself—famed in the 1900s for its tea exports—is today best known for its prodigious tuna haul, the biggest in Japan, samples of which can be enjoyed in many of the port’s fantastic restaurants along with other local delicacies such as sakura shrimp and shirasu (whitebait).

Day 3: At Sea

Day 4: Takamatsu, Japan

Founded in 1890, Takamatsu is home to the Ritsurin Garden, created by an Edo-era feudal lord. This magical place comes to life with cherry blossoms in the spring and brilliant color in the fall.

Days 5 & 6: Kobe, Japan

One of the greatest things about Japan is its attention to detail. Nothing is too small for consideration. Nailheads on temple walkways are hidden by inlaid metal covers. If the train schedule says the train arrives at 11:05, it will not be there at 11:04; and if it’s more than 10 minutes late, you can get the rail line to give you an excuse form to present back at the office, explaining your tardiness. Shops sell combs and hairpins made with the same patterns and in the same way as 500 years ago.

So maybe this attention to detail explains what happened in 20th-century Kobe. Some farmer was looking at his cow, thinking, “What possibilities of perfection am I missing?” Cows were still a new thing; they were banned as food almost until WWII, so cow rules were in flux when this farmer began massaging his herd with sake. The cows got pleasantly drunk on local beer and listened to classical music—and in return for the pampering, they produced, and continue to produce, heavily marbled, melt-in-the-mouth cuts of meat that can easily sell for a hundred bucks a dish. Like everything else in town, Kobe beef is all in the details.

Day 7: Kochi, Japan

High atop a hill in Kochi sits 17th-century Kochi Castle, once the seat of the Yamauchi lords. Explore this historic site and enjoy panoramic views of the city, then dine on sushi at Hirome Market.

Day 8: Scenic Cruising Kanmon Strait

The Kanmon Strait is a narrow channel of water that separates two of Japan's main islands, Honshu and Kyushu. The channel has long been important to maritime transportation and cargo ships, as it connects the Sea of Japan and the Inland Sea. Passenger and car ferries link the port cities of Shimonoseki and Kitakyushu, as do trains and bridges. The battle between the U.S. and Japanese navies that presaged the Shimonoseki Campaign in 1863 took place here, and eventually led to Japan's opening up to Western powers. The cannons used during the campaign can today be seen near Shimonoseki’s port, where you can also dine at gourmet restaurants serving local delicacies such as fugu (blowfish), shop at venues like the Sea Mall, and connect with ferry service to Busan, in South Korea, and the island of Kyushu.The port at Kitakyushu (Moji Port) is equally historic and attractive, serving as a gateway to Honshu and Kyushu for centuries as well as an important international trade hub since the late 19th century. Although more industrial than Shimonoseki, it has many Western-style buildings, including the neo-Renaissance Mojiko Station, constructed in 1914, as well as other tourist attractions such as a developed promenade and the Kawachi Fuji Gardens. A highlight of the Kanmon Strait is an annual fireworks display—the largest in Japan—with more than 13,000 rockets fired from both sides of the strait. The spectacle draws more than a million visitors every August.

Day 9: Tsuruga, Japan

This sleepy little port city is home to the intimate Kehi Shrine, with its red-lacquered Torii gate and koi pond. Learn about the fascinating history of the town at the Tsuruga Museum. Dine on grilled seafood like a local at Nihonkai Sakana Machi.

Day 10: Sakaiminato, Japan

Sakaiminato is home to Shigeru Mizuki, creator of GeGeGe no Kitaro (a character who’s everywhere in contemporary Japan), and gateway to the ancient region of Honshu, site of the famous “Black Castle.”

Day 11: Busan (Pusan), South Korea

South Korea’s second-largest city (after the capital, Seoul), Busan is located in the southeastern corner of the country along the Sea of Japan. It combines a vibrant, big-city atmosphere with a famously laid-back attitude and subtropical landscapes. Often described as the "San Francisco of Korea," thanks mainly to its hilly terrain and close-knit neighborhoods, it offers visitors a little of everything: fashionable boutiques, dynamic culture and buzzy nightlife, as well as sandy beaches, hot springs and nearby mountains crossed with hiking trails and dotted with temples. Cultural highlights include the Gamcheon Cultural Village; the spectacular Haedong Yonggungsa Temple, built into the side of a cliff; and Art Street in Sinchang-dong, which hosts art competitions, exhibitions and cultural events such as the annual Busan International Film Festival. Those who enjoy hiking can explore the famed cliffs of Taejongdae Park, while the white sand beaches at Gwangalli and Haeundae are ideal places to relax by the seashore. Foodies will love Busan, too, not just for its excellent restaurants but also for the many atmospheric markets: the low-key Millak Hoe Town Market, tourist spots like Jagalchi Fish Market and the market at Haeundae with its ramshackle stalls selling gukpab (a traditional rice soup).

Day 12: Jeju (Cheju) City, South Korea

Jeju, formerly Cheju, may not be familiar to most Americans, but for Korean travelers the country’s largest island and home to one of 12 UNESCO World Heritage Sites is a popular destination. The island is roughly the size of Maui and has much in common with the Hawaiian islands. Like them, it is a volcanic island—it first emerged from the sea some two million years ago and the volcano Hallasan, which reaches a height of 1,950 meters, is the tallest peak in South Korea. It also shares the mild subtropical climate of Hawaii—even in winter, temperatures rarely drop below freezing—and offers a similar broad range of activities whether in the warm ocean water or exploring the island’s interior on well-marked and maintained trails.

Day 13: Kagoshima, Japan

Situated at the southern tip of Japan, Kagoshima is the capital of the prefecture of the same name and famous for its dramatic views of Sakurajima, an active volcano that smolders across the bay. One of the most popular activities is taking a ferry to Sakurajima and hiking on the 100-year-old lava flow that is now a grassy peninsula. Kagoshima, however, offers much more than the volcano’s almost overwhelming beauty. The food scene provides opportunities to experience the area’s rich culinary culture and features dishes using locally caught fish and regional specialties, like satsuma a’ge (deep-fried fish cake) and shōchū, a traditional beverage made at more than 100 distilleries in Kagoshima alone. Although the city was officially founded in 1889, it has an even longer history that is reflected in the 17th-century gardens of Sengan-en. More recent events are covered at a museum dedicated to the kamikaze pilots who flew out of Kagoshima. Other popular attractions include the City Aquarium, the Museum of the Meiji Restoration with its exhibits exploring local history and the City Museum of Art with its collection that covers both local contemporary and older art. With so much to do, visitors may want to consider the Cute transit card. Available at tourist information offices, one-day Cute cards cover city buses, trams and Sakurajima ferries and also provide discounted admission to several attractions.

Day 14: At Sea

Day 15: Yokohama (Tokyo), Japan

From Yokohama, it’s a quick trip to peaceful Kamakura, home to Daibutsu, Japan’s second-largest bronze Buddha, and to the important Shinto shrine Tsurugaoka Hachimangu. Head to Hakone National Park on a clear day and you’ll be rewarded with picture-postcard views of majestic Mt. Fuji.