Crocodile Dundee, shrimp on the barbie, kangaroos, Olympic swimmers and “Waltzing Matilda.” Until recently, the impressions that most Americans had of the distant continent and country of Australia were based on the stereotypes of 20th-century pop culture. Australia has gradually emerged on the global scene as one of the world’s top dozen economies and an increasingly popular tourist destination. British, Chinese and American tourists have been visiting the country on group tours and cruises to enjoy the unusual landscapes, modern cities, outdoor living and friendly people that this unique destination has to offer.

Planning a trip to Australia requires prioritization. The vastness of the country’s rugged interior and the concentration of two-thirds of the population in six coastal cities means that it would take a lot of airplane rides to see all of the country’s principal sites. Some people are drawn to the Cairns area in the tropical northeast to scuba dive or view the wonders of the Great Barrier Reef, while others challenge the outback by flying into Alice Springs or Darwin. Another popular destination is the southern island of Tasmania, which has a temperate climate like the British Isles. Tasmania once served as the landing point for many of the 200,000 people who were “transported” from overcrowded British prisons to Australia between 1788 and 1868 for a lifetime of servitude or eventual freedom in a strange new land.

We decided to limit our two-week trip to the southeastern quadrant of the country and to use the cities of Brisbane, Sydney and Melbourne as our bases for excursions to the many interesting places to see nearby. Some of the best places to see there include the following:

Brisbane and the Gold Coast: Brisbane often gets ignored by tourists who limit their stops to the two major Australian cities of Sydney and Melbourne. But this east coast city is a great place to begin a visit to Australia. It is a manageable city of 2.1 million people, with a compact downtown shopping district and magnificent riverfront attractions.

The South Bank of the Brisbane River can be reached by walking across several bridges. Once there, you will find a performing arts center, art galleries, a science museum, maritime museum, and a Ferris wheel, as well as a variety of restaurants, cafés and parks along shaded walkways. One of the unique features of the South Bank is the Streets Beach, a public lagoon and artificial beach as large as five Olympic pools. The South Bank is a great place to relax during the afternoon or take an evening stroll.

Brisbane provides ready access to a variety of interesting places. Few visitors miss the Lone Pine Koala Sanctuary, which can be reached by a pleasant ferry ride up river. The sanctuary has troops of kangaroos, reptiles, dingoes, Tasmanian devils and other unique Australian wildlife to view and feed. But the star attraction is the more than 100 koala bears that are lovingly displayed clinging to eucalyptus trees or available for holding and photographing on a limited basis. Another popular destination is the beachfront community of Byron Bay, which is a two-hour drive down the coast. Once a hippie town, Byron Bay has become more of a New Age, upscale community with spas, beautiful beaches and a famous lighthouse that attracts day trippers of all ages.

South of Brisbane is a 40-mile stretch of beachfront condominiums, theme parks and resort hotels known as the Gold Coast. While the ambience is more like South Florida and Southern California than the Jersey shore, the Gold Coast has a mixed reputation among Australians. Nevertheless, it is the fastest growing area of the country and worth a couple days if you need to unwind after the long airline flight or to spend a couple of beach days in country. We stayed at a resort in Main Beach and took in a dinner show nearby known as the “Australian Outback Spectacular”; it featured a cowboy-themed horse show and patriotic skits about the 500,000 ANZAC soldiers who fought hard alongside the Allies in World War I.

Sydney and the Blue Mountains: No visit to Australia would be complete without visiting the international city of Sydney and taking in the sites of its splendid harbor. Sydney was the site of the first British colony in Australia and was established only two decades after Captain James Cook surveyed the east coast of the continent on his exploration voyage of 1768. Expecting a paradise, the First Fleet of 11 ships arrived from England with 750 convicts, 200 soldiers and 40 women and children in 1788. They endured poor supplies, tough soil and harsh conditions for the first several decades in the new land.

Today, Sydney is a hip city with neighborhoods and villages spread all around the many coves located on the harbor. The two signature sites on the waterfront are the Sydney Opera House, a performing arts center shaped like sea shells and the sails of a ship, and the single span Harbour Bridge that connects both sides of the harbor. The best way to view these wonders is from a ferry such as the one which connects downtown with Manly Beach, a relaxing place to take in the sun, dine or shop for a day. Other popular destinations in the city include the observation decks and restaurants in Sydney Tower, as well as several interesting museums that depict the natural and historical wonders of the country, and the 60,000-year existence of the Aboriginal tribes that comprise about three percent of Australia’s population.

The best day trip out of Sydney is to take a two-hour train ride to the Blue Mountain National Park. Most of the best sites are located near the small towns of Katoomba and Leura, where one can see blue-tinted gorges, plateaus and waterfalls that amazed early settlers and physically blocked them from reaching the fertile plains to the west for several decades. You can enjoy the outdoor scenery at Katoomba by simply visiting the viewing platform above the famous rock formation known as the “Three Sisters,” riding a small railway that plunges down into the valley, rising above the mountains on the Scenic Skyway, or hiking the trails. While the shopping, cafés and hotels are nothing to write home about, there is an excellent bus service known as the Blue Mountain Explorer Bus available at the Katoomba railroad station that provides guided transportation to the key sites with stops at 29 locations.

Melbourne and the Gold Territory: For much of Australia’s early history, Melbourne was its principal city. The gold rush that took place throughout the territory of Victoria in the 1850s was a boon for the entire region, and Melbourne served as the nation’s capital until Canberra was built halfway between Sydney and Melbourne in 1927. As the years went by, Australia’s two largest cities have continued to be rivals, with each one hosting the Olympic Games, World Expositions and international conventions.

As in Sydney and Brisbane, most tourist activity in Melbourne is centered around the Yarra River that empties into Port Phillip Bay. A convenient trolley system allows people to visit downtown malls, museums, a botanical garden and riverfront attractions. Prominent entertainment venues along the river include a large Crown Casino complex, a Ferris wheel and dozens of restaurants. Sports are also a major attraction in Melbourne, since it hosts the Australian Tennis Open for two weeks every January and draws large crowds for professional cricket, rugby, Australian Rules football and a Formula One Grand Prix race.

There are two popular excursions from Melbourne. One is to visit the historic mining city of Ballarat, which is located about an hour away and has a Mystic Seaport type village known as Sovereign Hill. At Sovereign Hill, visitors can pan for gold, see a real gold bar pour and visit a still-active mine. The other place to see is the Phillips Island Nature Park, which serves as a sanctuary for penguins and other native creatures. At Phillips Island, you can learn about this popular bird and watch hundreds of them come ashore to their burrows on the island beach at sunset.