National Congress of Brazil
Brazil's capital was once the socially stratified Rio de Janeiro, with the affluent near the beach and the poor in hillside shanties. Then President Juscelino Kubitschek had a mind to change all that, and in 1960 his Le Corbusier–inspired utopia in the country's remote interior became a reality. Standing at its center is Oscar Niemeyer's National Congress of Brazil, a legislative complex with hemispheric assembly rooms and twin office towers. These and other idealistic structures still stand, but Kubitschek's egalitarian dreams were not as durable. These days, much of the city is a slum, and visitors—whether here on political or architectural pilgrimage—rarely linger. For those in the latter camp, the hotel to beat is the mid-century-modern-inspired Blue Tree Towers Brasília, next to Niemeyer's sleek marble-and-concrete presidential palace (55-61-3429-8000; bluetree.com.br; doubles, $160-$192).

Pudong New Area
China's richest city in the first part of the last century, Shanghai lost its luster under Mao. Today, under the aegis of the Central Committee of China's Communist party, its Pudong financial district is the engine that powers the rest of the country—thanks to liberal laws allowing building at a rate unseen in Western countries. Stay in another Pudong landmark, the Jin Mao Tower, where the Shanghai Grand Hyatt occupies floors 53 to 87 (86-21-5049-1234; shanghai.grand.hyatt.com; doubles, $252–$394). And get a glimpse of what the future holds at the Shanghai Urban Planning Exhibition Center, where the city of 2020 sprawls in a scale model (100 Renmin Dadao, People's Sq.; 86-21-6318-4477).

Jumeirah Beach Hotel
Around the time of the first Gulf War, petrol-rich Dubai looked at its dwindling oil and gas reserves and decided that its future lay not in fuel but in tourism. Almost two decades later, Sheikh Maktoum bin Rashid Al Maktoum (now deceased) and his brother Sheikh Mohammed bin Rashid Al Maktoum (the current ruler) have turned the kingdom into a major destination. But construction is far from complete. Desert sands continue to be sculpted into artificial islands, and cranes assembling the latest skyscrapers still punctuate the horizon. For this particular panorama, head to the rooftop restaurant of the iconic Burj Al Arab hotel (971-4-301-7777; burj-al-arab.com; suites, $2,315–$2,723), which overlooks its wave-shaped sister property, the Jumeirah Beach (971-4-348-0000; jumeirahbeachhotel.com; doubles, $817–$1,062).

Place de l'Étoile
When Napoleon III came to power in the mid-1800s, Paris was laid out much as it had been in the Middle Ages—and had many of the same social problems: overcrowding, poor sanitation, and rampant disease. The emperor tapped Baron Georges-Eugène Haussmann to help him refashion the city, demolishing neighborhoods and constructing a network of avenues with public squares. Twenty years and forty thousand buildings later—voilà: the Paris of our dreams, with broad boulevards of uniform facades with balconies and angled eaves. Twelve of these thoroughfares meet at the Place de l'étoile, Paris's largest intersection and site of the Arc de Triomphe, the Napoleonic War memorial whose observatory affords views of the avenue de la Grande Armée. Behind you, at the other end of the Champs-Élysées, the luxe Hôtel de Crillon predates nineteenth-century urban renewal, occupying one of two buildings Louis XV commissioned as government offices (33-1-44-71-15-00; crillon.com; doubles, $1,101–$1,366).