Fascinating limestone hills and towers lure tourists from China and around the world to this city of 630,000. Popular sights include 120-hectare Seven Star Park, Reed Flute Cave, 200-foot high Fubo Hill and the much-loved Elephant Trunk Hill. Guilin is very popular as a starting point for Li River cruises to Yangshuo and for visits to the nearby minority villages of Yao, Miao and Dong. April, May, September and October are the best months to visit, as they avoid the extremes of heat and rain.

Mumbai (formerly known as Bombay), India, is famous for its chaotic streets. For bargains and people-watching, outdoor bazaars top the list of attractions. Popular waterfront destinations are Marine Drive, where visitors go to watch the sun set over the Arabian Sea, and the carnival-like Juhu Beach. More sightseeing options are the Gandhi Museum, in the leader's former home, and the cave temples of Elephanta Island. For tranquillity, Mumbai has many religious sites, lakes and parks.

Serenely spiritual Dharamsala is home to the largest Tibetan temple outside of Tibet. It’s known for its religious iconography and is the monastery of the Dalai Lama, who holds public lectures a few times a year. Once you’ve restored your spiritual energy, enjoy a picturesque stroll to Bhagsu Waterfall or climb the hill to Triund to bask in stunning views of the Himalayas.

Founded in the mid-17th century as a winter quarters for traders and tax collectors, Irkutsk came to prominence in the 1800s. Participants in the Decembrist revolt against Tsar Nicholas I were exiled to Siberia in droves, turning Irkutsk into their cultural center. Today, it’s one of Siberia’s biggest and most important cities, with over half a million people, many universities, many historic churches and museums, and beautiful Lake Baikal, just about an hour away by train.

On the banks of the Volga River, Kazan sits austerely, its cityscape a visual confection of architecture that somehow manages to be both playful and severe. No matter your spiritual inclination, you simply must visit the Temple of All Religions, a Technicolor cultural center built by artist Ildar Khanov. Though still a work in progress, the "temple" is a feast for the eyes—and the spirit.