Day 1 Sydney, New South Wales, Australia

Sydney belongs to the exclusive club of cities that generate excitement. At the end of a marathon flight there's renewed vitality in the cabin as the plane circles the city, where thousands of yachts are suspended on the dark water and the sails of the Opera House glisten in the distance. Blessed with dazzling beaches and a sunny climate, Sydney is among the most beautiful cities on the planet.With 4.6 million people, Sydney is the biggest and most cosmopolitan city in Australia. A wave of immigration from the 1950s has seen the Anglo-Irish immigrants who made up the city's original population joined by Italians, Greeks, Turks, Lebanese, Chinese, Vietnamese, Thais, and Indonesians. This intermingling has created a cultural vibrancy and energy—and a culinary repertoire—that was missing only a generation ago.Sydneysiders embrace their harbor with a passion. Indented with numerous bays and beaches, Sydney Harbour is the presiding icon for the city, and urban Australia. Captain Arthur Phillip, commander of the 11-ship First Fleet, wrote in his diary when he first set eyes on the harbor on January 26, 1788: "We had the satisfaction of finding the finest harbor in the world."Although a visit to Sydney is an essential part of an Australian experience, the city is no more representative of Australia than Los Angeles is of the United States. Sydney has joined the ranks of the great cities whose characters are essentially international. What Sydney offers is style, sophistication, and great looks—an exhilarating prelude to the continent at its back door.

Day 3 Burnie, Tasmania, Australia

Burnie overlooks Emu Bay, on the north-west coast. This proudly industrial city is Australia's fifth largest container port and a vibrant place to visit. Burnie was once surrounded by dense rainforest, but this has slowly disappeared, while fortunes were made felling and milling timber. The paper and pulp mill on the city's outskirts operated from 1938 to 1998. Burnie was first explored by Bass and Flinders and was known as Emu Bay when it was settled by the Van Diemen's Land Company in 1827. Today, Burnie has a population of almost 19,000. Burnie experiences temperate conditions, with an average maximum of 70 degrees Fahrenheit (21 degrees Celsius) in January and 56.5 degrees Fahrenheit (13.5) degrees Celsius in June.

Day 4 Melbourne, Victoria, Australia

Consistently rated among the "world's most livable cities" in quality-of-life surveys, Melbourne is built on a coastal plain at the top of the giant horseshoe of Port Phillip Bay. The city center is an orderly grid of streets where the state parliament, banks, multinational corporations, and splendid Victorian buildings that sprang up in the wake of the gold rush now stand. This is Melbourne's heart, which you can explore at a leisurely pace in a couple of days.In Southbank, one of the newer precincts south of the city center, the Southgate development of bars, restaurants, and shops has refocused Melbourne's vision on the Yarra River. Once a blighted stretch of factories and run-down warehouses, the southern bank of the river is now a vibrant, exciting part of the city, and the river itself is finally taking its rightful place in Melbourne's psyche.Just a hop away, Federation Square—with its host of galleries—has become a civic landmark for Melburnians. Stroll along the Esplanade in the suburb of St. Kilda, amble past the elegant houses of East Melbourne, enjoy the shops and cafés in Fitzroy or Carlton, rub shoulders with locals at the Victoria Market, nip into the Windsor for afternoon tea, or rent a canoe at Studley Park to paddle along one of the prettiest stretches of the Yarra—and you may discover Melbourne's soul as well as its heart.

Day 6 Adelaide, South Australia, Australia

Australians think of Adelaide as a city of churches, but Adelaide has outgrown its reputation as a sleepy country town dotted with cathedrals and spires. The Adelaide of this millennium is infinitely more complex, with a large, multiethnic population and thriving urban art and music scenes supported by a "space activation program" that encourages pop-up shops, markets, performances, street food, mini festivals, art exhibitions, and other "off-the-cuff" experiences in the cities underutilized streets and public spaces.Bright and clean, leafy and beautiful Adelaide is a breeze to explore, with a grid pattern of streets encircled by parkland. The heart of the greenbelt is divided by the meandering River Torrens, which passes the Festival Centre in its prettiest stretch.

Day 10 Fremantle, Western Australia, Australia

The port city of Fremantle is a jewel in Western Australia's crown, largely because of its colonial architectural heritage and hippy vibe. Freo (as the locals call it) is a city of largely friendly, interesting, and sometimes eccentric residents supportive of busking, street art, and alfresco dining. Like all great port cities, Freo is cosmopolitan, with mariners from all parts of the world strolling the streets—including thousands of U.S. Navy personnel on rest and recreation throughout the year. It's also a good jumping-off point for a day trip to Rottnest Island, where lovely beaches, rocky coves, and unique wallaby-like inhabitants called quokkas set the scene.Modern Fremantle is a far cry from the barren, sandy plain that greeted the first wave of English settlers back in 1829 at the newly constituted Swan River Colony. Most were city dwellers, and after five months at sea in sailing ships they landed on salt-marsh flats that sorely tested their fortitude. Living in tents with packing cases for chairs, they found no edible crops, and the nearest freshwater was a distant 51 km (32 miles)—and a tortuous trip up the waters of the Swan. As a result they soon moved the settlement upriver to the vicinity of present-day Perth.Fremantle remained the principal port, and many attractive limestone buildings were built to service the port traders. Australia's 1987 defense of the America's Cup—held in waters off Fremantle—triggered a major restoration of the colonial streetscapes. In the leafy suburbs nearly every other house is a restored 19th-century gem.

Day 14 Benoa, Bali, Indonesia

Bali really is as alluring as everyone says. This island, slightly bigger than Delaware, has it all: beaches, volcanoes, terraced rice fields, forests, renowned resorts, surfing, golf, and world-class dive sites. But what sets Bali apart from other nearby tropical destinations is Balinese tradition, and villagers dedicated to celebrating it. The hundreds of temples, dances, rituals, and crafts linked to their ancient Hindu faith aren't a show for tourists, but a living, breathing culture in which visitors are warmly received by the Balinese, who cherish their own identities.

Day 18 Port Klang, Malaysia

Kuala Lumpur, or KL as locals refer to it, intrigues visitors with its diversity and multicultural character. The city's old quarter features stretches of shop houses that hint at its colonial past, while modern buildings—including the iconic Petronas Towers—give a glimpse of its modern financial ambitions. The city is filled with culturally colorful quarters dedicated to Chinese, Malay, and Indian communities. New shopping malls with designer labels, five-star hotels, and top-notch restaurants also proliferate in this bustling city of 1.6 million.

Day 19 Georgetown, Penang, Malaysia

An island off the northwest coast of peninsular Malaysia, Penang is blessed with a multicultural history that's led to a fascinating fusion of East and West. Claimed by the British East India Company in 1786, the island's city center of Georgetown—listed as a UNESCO World Heritage Site—is filled with colonial architecture, temples, and museums. The island has also attracted many Chinese immigrants, who now make up the majority of the population. On Penang you'll find an exciting mix of jungle, coast, farmland, and fishing villages, along with the country's largest Buddhist temple.

Day 21 Singapore, Singapore

The main island of Singapore is shaped like a flattened diamond, 42 km (26 miles) east to west and 23 km (14 miles) north to south. Near the northern peak is the causeway leading to West Malaysia—Kuala Lumpur is less than four hours away by car. It is at the southern foot where you will find most of the city-state's action, with its gleaming office towers, working docks, and futuristic "supertrees," which are solar-powered and serve as vertical gardens. Offshore are Sentosa and over 60 smaller islands, most uninhabited, that serve as bases for oil refining or as playgrounds and beach escapes from the city. To the east is Changi International Airport, connected to the city by metro, bus, and a tree-lined parkway. Of the island's total land area, more than half is built up, with the balance made up of parkland, farmland, plantations, swamp areas, and rain forest. Well-paved roads connect all parts of the island, and Singapore city has an excellent, and constantly expanding, public transportation system. The heart of Singapore's history and its modern wealth are in and around the Central Business District. The area includes the skyscrapers in the Central Business District, the 19th-century Raffles Hotel, the convention centers of Marina Square, on up to the top of Ft. Canning. Although most of old Singapore has been knocked down to make way for the modern city, most colonial landmarks have been preserved in the CBD, including early-19th-century buildings designed by the Irish architect George Coleman.