One of southeastern Sicily’s UNESCO-listed baroque cities, Noto is famed for its opulent architecture and surfeit of beauty. Its 18th-century cathedral is a local highlight, as is Caffe Sicilia, which is rumored to make some of the best gelato in all of Italy.

The Mediterranean's biggest island is separated from the mainland by the Strait of Messina. A mountainous spot, Sicily's coast and its small islands sit at the foot of volcanoes, including Etna, Stromboli and Vulcano. The Greeks, Romans, Normans and Catalans all left their mark on the island in the form of Byzantine palaces, Gothic castles and Baroque flourishes in capital Palermo. Most larger towns offer interesting museums, but Etna and the Hellenic temples in Agrigento offer particularly unique sights.

If you currently think your neighbourhood coffee shop is nice, you might want to stay out of Vienna’s coffeehouses. After you’ve gotten used to these palatial, yet welcoming cafes—and their delicious coffee and Sacher torte—your local café will pale in comparison. Between coffee breaks, visitors can explore Vienna’s Schonbrunn Palace and Imperial Palace. And if you have a chance, catch a performance at the State Opera House—it’s not to be missed.

The prophet Mohammed's birthplace is Islam's spiritual center and is strictly off-limits to non-Muslims. The pillars of Islam state that all Muslims with the means must undertake Hajj, a pilgrimage to Mecca, once in their lifetime. Those who visit the holy city are rewarded not just by proximity to landmarks and religious sites crucial to the religion, such as the Masjid Al Haram (Holy Mosque), the Mountain of Light, the Black Stone and the Well of Zamzam, but with the forgiveness of all their sins.

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.

East meets West in this sun-soaked state, where Indian culture intertwines with Portuguese influences left over from a 500-year occupation. The beaches have long served as a magnet for serene hedonists. To the north, the tourist-centric scene is prevalent, with an international flair that is now skewing more hip than hippie. Travel south for stretches of unspoiled sand and an escape from large resorts. Temples, mosques and wildlife sanctuaries provide diversions from the beach.

Want a taste of being royal? Eat in Hyderabad, where culinary traditions have been passed down from the Nizam monarchy. Arabic, Turkish and Mughlai influences are easily recognisable. The city is famous for its rich, aromatic biryani made with lamb, chicken or vegetables and served with fragrant basmati rice. Satisfy your sweet tooth with double-ka-meetha, a bread pudding.

Known as both the "Garden City" and "The Silicon Valley of India," Bangalore (officially "Bengaluru") is a techie’s paradise, boasting the highest concentration of IT companies in the country. When you’re done geeking out, there are plenty of gardens, museums, natural features, palaces and temples to fill your dance card. Visit Vidhana Soudha, Cubbon Park and the Ulsoor Lake of Bangalore, well known for its beautiful locales and boating facilities. Bangalore is also a major centre of Indian classical music and dance, and of vivid, cutting-edge nightlife.

Darjeeling, nestled among rolling mountains, is a perfect destination for outdoor enthusiasts. Popular places to visit include Tiger Hill, Batasia Loop and the War Memorial, and the Himalayan Zoological Park and Snow Leopard Breeding Center. What should you bring home? Tea, tea, and more tea—and beautiful local handicrafts.

The people of Tamil Nadu consider providing food to others a service to humanity. Thus the service in the state capital, Chennai, is first-rate. Treat your senses to some of the richest South Indian flavours in traditional dishes like sambar, rasam, fish curry or kootu. And don't forget to have a cup of full-bodied Tamil coffee, enhanced with chicory—no visit is complete without it.