Baguio, perched high in the Cordillera Central Mountains, is a great place to escape the heat of the Philippine lowlands. Camp John Hay, originally built as a recreation area for U.S. soldiers, now is a full-fledged resort complete with a world-class golf course. Definitely stop at the city market, where you can buy almost anything (just be prepared to haggle).

Perched on Sri Lanka’s southwest coast, Galle wears its history on its sleeve. Windswept beaches and nodding palms surround its colonial-era showpiece, a 16th-century Portuguese-built fort, while the rest of the city is trimmed with Dutch-style houses, quirky shops, whitewashed mansions, and heritage museums.

New Delhi is all at once chaotic and calm, a complicated city where cows often wander the shanty-lined streets. The 17th century Red Fort is a mass of domes and turrets, while Chandni Chowk is an exercise in friendly haggling. Jantar Mantar features larger-than-life sundials and astronomical instruments that are still used to predict the weather. Travelers and locals flock to the India Gate, the national monument of India that honors the soldiers who died in World War I and the Third Afghan War.