Walk atop Rothenburg’s city walls or climb to the top of the town hall for great views. The Night Watchman tour is an unforgettable way to learn the city’s history. And our travelers also recommend the Medieval Crime Museum (Mittelalterliches Kriminalmuseum)—it’s gruesome but fascinating.

Home to the oldest university in Germany, Heidelberg was hit hard during 17th-century wars and rebuilt in the 18th century with baroque buildings. For a pleasant walk, stroll through the historic city centre's Gothic streets. Be sure to take in Heidelberg Castle, the symbolic heart of the city; Alte Brucke, a beautiful 18th-century bridge; and the Student Jail. Built as long ago as the 16th century, it was used to keep mischievous students off the streets for three days to a month at a time. And they say Penn State is the number-one party school!

Like Rothenburg, Dinkelsbuehl is one of the smaller mediaeval fortress cities. With its walls and towers still intact, it has the look of a typical German town of the 15th to early 17th century. Sample the famous German cuisine served in larger cities, but without the crowds. Don't miss the annual summer celebration, marking the city's surrender to Swedish troops during the Thirty Years' War. The event is emphatically reenacted by many of the town's residents. And really, who doesn't love amateur theatre?

About 10 miles north of Nuremberg, Erlangen is the home of the University of Erlangen-Nuremberg (Friedrich-Alexander-University), founded in 1742. Just over 100,000 people live here, about a third of whom are involved with the university; about another third work for the Siemens corporation. Bergkirchweih, Erlangen’s annual festival - akin to Munich’s Oktoberfest - opens in a different beer cellar every year and is attended by over a million people in its twelve-day run around Pentecost.

In 1715, margrave Karl III Wilhelm decided he needed more space than he had in Durlach, so he moved his capital to Karlsruhe and had it designed in circular spokes around his new palace. Because of its unique radial shape, Karlsruhe is sometimes called the “fan city.” Home to Germany’s most important federal courts, the city accordingly teems with civil servants. Karlsruhe Schloss (castle) was badly damaged in World War II, but was rebuilt and is now home to the Badisches Landesmuseum.

Laid out by British architect Edwin Lutyens, the Indian capital is a striking modern metropolis. A gracious contrast to Old Delhi's winding streets, the grand avenues and stately buildings of New Delhi are rich with history and culture, from Gandhi's Delhi home (and the site of his assassination) to the tomb of Humayun, a complex of Mughal buildings reminiscent of the Taj Mahal. Chaotic traffic is best left to the locals. Negotiate a good price for taxis or travel on the new Delhi Metro.

The north Indian city of Varanasi, or Benares, is regarded as sacred by Hindus, Buddhists and Jains. Situated in the fertile Ganga valley and on the banks of the Ganges, Varanasi is a place of pilgrimage for Hindus, who come to bathe in the holy river. Known as the City of Temples and a beacon of culture, Varanasi has produced many renowned writers. It’s also a centre of silk weaving, so practise haggling at the chaotic bazaar for some beautiful souvenirs. Rickshaws are the best way to get about.

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.

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.