The Blue Mountains are named for the delicate azure haze that lingers along the region, which is actually a fine cloud of oil emitted by eucalyptus trees. The mystical mountains are a labyrinth of plateaus, gorges and gum trees. Check out the Katoomba Scenic Railway (the steepest railway in the world), the Jenolan Caves and the Giant Staircase nature walk.

Bordering Australia’s New South Wales' coast, just north of Sydney, sunny-natured Newcastle is anchored in indigenous and convict history. Surfing beaches, hand-cut sea pools, a coastal fort, and contemporary bars skirt the city’s harbour, while museums, artisanal restaurants, and microbreweries lie at its heart.

A gateway to Fjordland National Park, the quaint and peaceful township of Te Anau is nestled on the edge of a lake of the same name—the perfect site for jetboating or fishing. Embark on one of many day-long or multi-day hiking or walking tracks, then return to town to restore your body with a soak or massage at a spa and a delicious café meal. Nature lovers will marvel at the Te Anau glowworm caves, the Wildlife Park and Ivon Wilson Park, where rare Takahe birds flutter freely.

Staggering beauty and heart-pumping thrills await in the resort town of Queenstown, which is also known for its Hobbits—much of the Lord of the Rings trilogy was filmed in the area. Outdoor enthusiasts flock to Queenstown for the kayaking, bungee jumping, jetboating, white-water rafting, hiking and skiing. More mild-mannered adventurers can take a quiet cruise through nearby Milford Sound, part of the Fjordland National Park World Heritage area, or sample South Island pinot noir from one of the region's 75 wineries.

European, Polynesian, Asian and strong Maori heritages give the Auckland its distinctive culture. Discover the history of the world's largest Polynesian city through Maori treasures at Auckland Museum and experience the lives of 19th-century settlers at Howick Historical Village. Find Polynesian handicrafts at Otara Market or people-watch in bustling Ponsonby and Parnell. Adventure junkies can get their fix from kayaking, sailing and high-octane bungee jumping.

The Māori call Auckland Tāmaki Makaurau — a maiden desired by 100 lovers, and a valuable territory fought over for centuries for its fertile land and natural harbours on the Pacific Ocean (to the east) and Tasman Sea (to the west). Today, it’s New Zealand’s largest city: A vibrant and diverse place where nature and urban life go hand-in- hand, with 48 volcanic cones, more than 50 islands, and 29,000 km of coastline and beaches just minutes away from the arts and shopping of the central city.

Bubbling mineral springs and pools promise maximum relaxation in Rotorua, on New Zealand's North Island. Therapeutic hot mud pools, dramatic geysers and a buried village are within easy reach of the city. What happens in the bubbling mud geysers of "Rotovegas"—the area at the top of Fenton Street—stays in Rotovegas. Once you've made the most of the mud, soar nearly 2,000 feet on the Skyline Gondola for views of Lake Rotorua, then zip back down to explore the lake by paddle steamer, fishing charter or WWII amphibious vehicle.

Singapore is known as a bustling metropolis that also happens to be one of the cleanest and safest cities of its size in the world. (Just make sure you heed the local laws—something like spitting in the street might merely be considered rude in your hometown, but here, it carries a severe penalty.) You'll find historic sites like the Thian Hock Keng temple, superlative shopping (including gargantuan malls) and numerous beaches.

Tradition collides with pop culture in Tokyo, where you can reverently wander ancient temples before rocking out at a karaoke bar. Wake up before the sun to catch the lively fish auction at the Toyosu Market, then refresh with a walk beneath the cherry blossom trees that line the Sumida River. Spend some time in the beautiful East Gardens of the Imperial Palace, then brush up on your Japanese history at the Edo-Tokyo Museum. Don’t forget to eat as much sushi, udon noodles, and wagashi (Japanese sweets) as your belly can handle.