You can eat very well—and very cheaply—in Taipei. The restaurants may not look posh, but the quality of the food is superlative. And there’s a huge variety of restaurants—in addition to local Taiwanese specialties, you’ll find regional cuisines from all over China, as well as great Indian, Japanese and even Italian options. Just make sure to leave some room for snacks—street-vendor food here is addictive.

Go from the 13th century to the 21st in one day in Naha. Its ancient Ryukyu Kingdom centrepiece, Shuri Castle, has been restored and is the city's top tourist attraction. Meanwhile, on Kokusai-dori (International Boulevard), the pace never lets up as locals and tourists hop from restaurants to bars to nightclubs.

Hong Kong's a great city for an adventurous eater. Stop at a street vendor for fish balls on a stick or stinky tofu. Bakeries offer wife cake, pineapple buns and egg tarts. Or opt for as much dim sum as you can eat. If you're tired of local and regional Chinese specialties, check out upscale offerings from some of the world's top chefs, like Joel Robouchon and Alain Ducasse.

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.

Dubai is a destination that mixes modern culture with history, adventure with world-class shopping and entertainment. Catch a show at the Dubai Opera, see downtown from atop the Burj Khalifa and spend an afternoon along Dubai Creek exploring the gold, textile and spice souks. If you’re looking for thrills, you can float above the desert dunes in a hot air balloon, climb aboard a high-speed ride at IMG Worlds of Adventure or skydive over the Palm Jumeirah.

The second largest city in Russia, St. Petersburg is the country’s cultural heart. View splendid architectural gems like the Winter Palace and the Kazan Cathedral, and give yourself plenty of time to browse the world-renowned art collection of the Hermitage. Sprawling across the Neva River delta, St. Petersburg offers enough art, nightlife, fine dining and cultural destinations for many repeat visits.

City slickers, culture vultures and beach bums alike fall in love with Sydney. Hang ten at famed Bondi Beach or stroll the calmer sands of Coogee.  Cash burning a hole in your pocket? You’ll find great shopping in the Rocks district and along George and Pitt Streets. Climb to the top of the Harbour Bridge or take a skywalk on Sydney Tower for a 360-degree view of the city. But whatever you do, don’t leave town without cuddling the koalas in the Taronga Park Zoo—they’re ridiculously adorable.