22-Day Grand World Voyage

City-states are rare in the present day—and none are quite like Singapore. In the 20th century, the Southeast Asian nation hurtled itself into the modern world, and it continues to expand its state-of-the-art transportation system and build its edgy skyline. Yet Singapore's urban plan wisely maintained its intimate neighborhoods, many with streets lined with colorful shophouses (a type of building unique to parts of Asia, with businesses located on their ground floors and residences above). Add the city’s mix of ethnic groups—mainly Malays, Chinese and Indians—and you get a vibrant cultural scene that attracts a cosmopolitan, international community. Singapore's food scene—which is arguably the world's most dynamic and runs the gamut from beloved street hawkers to Michelin-starred venues—would merit a trip alone, as would its never-ending shopping options. But the city is also packed with world-class museums, many designed by celebrated architects, and it hosts many major international events, such as the Formula One Grand Prix. Yet only about half of the 720-square-kilometer (278-square-mile) island is developed, which leaves plenty of room for parks and open spaces such as the Bukit Timah Nature Reserve, where an old-growth forest still thrives.

As you travel from Port Kelang to Malaysia's capital, Kuala Lumpur, 37 kilometers (23 miles) to the northeast, it can be hard to believe that the city with a skyline of soaring towers was a small mining town for much of the 19th century. That changed beginning in 1880, when the British moved the capital of Malaya here. Yap Ah Loy—a Chinese-born émigré who rose from miner to political titan—and British politician Frank Swettenham were crucial in turning KL (as it's often called) into a true city. Their program of improvements, including establishing Kuala Lumpur’s first school and building a number of roads, continues to this day. For more than a century, Kuala Lumpur has been determined to become bigger and better. For all its focus on the future, Kuala Lumpur has preserved some rich historic architecture, including the cheerful Art Deco Central Market, the Mughal-style Old Railway Station and the Tudor Revival Royal Selangor Club. These colonial-era buildings contrast nicely with newer structures, among them the gleaming Petronas Towers, whose design is based on motifs found in Islamic art, and the National Museum, inspired by Malay imperial palaces. Eating is practically a national pastime in Malaysia, and KL has some of the country's top restaurants. You shouldn't leave without enjoying a meal of delicious Southeast Asian, Chinese or Peranakan (a Malay-Chinese fusion) dishes.

Malaysia is the very definition of multiethnic and multicultural: Its population is a mix of Chinese, Indians and ethnic Malays, and its art, food, culture and language are influenced by former Portuguese, Dutch and British colonizers. Nowhere is this more evident than in Penang, which was the British Empire’s first settlement in Southeast Asia—the beginning of more than 150 years of British rule, which ended in 1948. Penang is divided by the Strait of Malacca into Penang Island and, on the Malay Peninsula, Seberang Perai. It’s easy to while away a day in George Town, the island’s capital and a UNESCO World Heritage Site, visiting ornate historic houses, snapping pictures of its charming streets and breaking for spicy laksa (coconut-curry soup) and kopi peng (iced coffee with condensed milk). Beyond George Town, Penang has a number of natural gems, including the idyllic Monkey Beach—with its white sand, clear waters and the occasional macaque—and Tropical Spice Garden, a must for anyone with an interest in South Asian cooking. No matter where you go in Penang, you’ll find something delicious to eat, from the chicken wings at humble hawker centers to upmarket takes on Malaysian home cooking.

Situated off the west coast of Thailand in the Andaman Sea, Phuket is Thailand’s largest island. Gain an understanding of Phuket history at the Talang National Museum; marvel at the elaborate ornamental design of Wat Chalong, Phuket's most important Buddhist temple; and of course spend time on one of the islands many incredible world-class beaches. Sample shore excursions: Sea Canoe Adventure; Phang Nga Bay.

Off the beaten track and tranquil—those adjectives describe just part of the allure of Sri Lanka’s southeastern corner. This is a quiet, laid-back, rural region of sleepy villages, farms and seemingly endless golden-sand beaches fringed by coconut palms and fronting the Indian Ocean's cerulean waters. Beyond Hambantota's new world-class port, colorful fishing boats cluster in its small harbor; their bounty can be seen in the daily fish market. Much of this part of Sri Lanka was off-limits during the country's civil war; then, it was hit hard by the 2004 tsunami. Fortunately the region has mostly recovered and is now open to tourists, who are discovering its natural beauty and a Sri Lankan way of life that is fast disappearing.

Scarred by decades of civil war, Sri Lanka and its commercial capital, Colombo, are relatively new to modern-day tourism. But Colombo has been a crucial trading post for more than 2,000 years. The city rose to prominence as Sri Lanka's most important port town in the 16th century with the arrival of Portuguese fleets. After a period under Dutch rule, Ceylon—as Sri Lanka was then called—became part of the British Empire in 1802. Sri Lanka gained independence in 1948, but the country experienced intense unrest from 1983 until 2009, when Sri Lanka's civil war finally came to an end. Many visitors head for the pristine beaches or up to the mist-draped mountains of Sri Lanka's tea country, and find that Colombo merits more than just a quick stop. Development continues at breakneck speed here, with skyscrapers jostling for space alongside the elegant architecture of its colonial past. Bustling markets and newfangled shops rub shoulders with ancient temples and rich layers of history in this fascinating place.

Port Louis is the capital city of Mauritius, in the Indian Ocean. It's known for its French colonial architecture and the 19th-century Champ de Mars horse-racing track. The Caudan Waterfront is a lively dining and shopping precinct. Nearby, vendors sell local produce and handicrafts at the huge Central Market. The Blue Penny Museum focuses on the island’s colonial and maritime history, along with its culture.

Cape Town's spectacular setting on Table Bay, beneath the 1,082-meter (3,550-foot) Table Mountain and Lion's Head, seldom fails to take one's breath away, whether you are a local or a visitor. If Johannesburg is South Africa's New York, this port city of four million, settled by traders from the Dutch East India Company in 1652, is its San Francisco. With a rich array of restaurants, galleries, vineyards and countless beaches, as well as a Mediterranean climate, life on the Cape Peninsula, which stretches for some 70 kilometers (43 miles) from downtown to the most southerly point, Cape Point, is genteel and all about good, healthy living and staying outdoors as much as possible. The Table Bay side of the city, known for its luxurious seaview properties and bustling nightlife, is countered by equally intriguing False Bay, which lies behind Table Mountain and is home to quaint, cobblestoned fishing villages like Kalk Bay, as well as the city's famous penguin colony. There, too, you'll find the oldest (and some of the best) vineyards in Africa, such as Constantia Uitsig and Buitenverwachting. If you visit, though, be warned: Once might not be enough.

Cape Town's spectacular setting on Table Bay, beneath the 1,082-meter (3,550-foot) Table Mountain and Lion's Head, seldom fails to take one's breath away, whether you are a local or a visitor. If Johannesburg is South Africa's New York, this port city of four million, settled by traders from the Dutch East India Company in 1652, is its San Francisco. With a rich array of restaurants, galleries, vineyards and countless beaches, as well as a Mediterranean climate, life on the Cape Peninsula, which stretches for some 70 kilometers (43 miles) from downtown to the most southerly point, Cape Point, is genteel and all about good, healthy living and staying outdoors as much as possible. The Table Bay side of the city, known for its luxurious seaview properties and bustling nightlife, is countered by equally intriguing False Bay, which lies behind Table Mountain and is home to quaint, cobblestoned fishing villages like Kalk Bay, as well as the city's famous penguin colony. There, too, you'll find the oldest (and some of the best) vineyards in Africa, such as Constantia Uitsig and Buitenverwachting. If you visit, though, be warned: Once might not be enough.