Mexico City
The famed “many Mexicos” of this rich and diverse country are reflected in this teeming, chaotic, noisy, and colorful capital. The historic region, studded by lakes, is now a city of superlatives, rippling with many millions of lights by night, peppered with neighborhoods steeped in tradition such as Xochimilco and gleaming financial districts like Santa Fe, as well as the inevitable shanty towns that fringe its ever-expanding outskirts. Trendy art deco zones with cafés and boutiques compete with leafy bohemian neighborhoods such as Frida Kahlo’s Coyoacán and Polanco, a diverse area of the city that is now the magnet for upscale shopping and dining. Amid food stalls and street vendors vociferously hawking their wares, the heart of the Great Tenochtitlan resonates still with the violent and magnificent history of the conquest of the Americas, with the exposed ruins of the Aztec Templo Mayor elbow to elbow with the great Metropolitan Cathedral, the first on the continent, sun bleached and tilted picturesquely by quakes.

London
The United Kingdom’s capital city—covering 610 square miles (1,580 square kilometers)—is huge. Founded in A.D. 43, it’s also old. And powerful. London is a hub of culture, business, and politics—and center of the once glorious British Empire that can still throw its weight around the globe. Served by a fabulous subway system, numerous tour buses, and the iconic black taxis, London is not difficult to find your way around in. And despite the city’s enormity, the center is small enough to make walking a good option—just mind the warnings painted on the curb to look right when crossing the street. Drivers come at you, unexpectedly, along the left side of the road.

Rio de Janeiro
Marvelous city, full of a thousand charms,” sang Aurora Miranda, in a 1934 Carnival hit that’s now Rio de Janeiro’s anthem. To put this song to the test, each year as many people visit Rio as live there—riding cable cars up to Pão de Açúcar, and trams through Santa Teresa; going inside belle epoque palaces at Cinelândia, and pleasure palaces at Copacabana; climbing to the Rocinha favela (shanty town) by minivan, and to “Christ the Redeemer” by train; shouting samba lyrics at the Sambódromo parade grounds, and “gol!” at Maracanã soccer stadium. In any other city, this would be exceptional. In Rio, you still have 992 delights to go.

The Talmud teaches that “Ten measures of beauty descended on the world—nine were taken by Jerusalem, one by the rest of the world. There is no beauty like the beauty of Jerusalem.” Mark Twain, however, complained in The Innocents Abroad that, “The sights are too many. They swarm about you at every step; no single foot of ground in all Jerusalem or within its neighborhood seems to be without a stirring and important history of its own.” Since Twain’s visit to the Holy Land, more than a century of strife and division have imbued the ancient city, sacred to three major world religions, with contemporary drama and made it even more multicultural and significant than ever. Jerusalem today is a schizophrenic, volatile, and fascinating meeting of ancient and modern, Israeli and Arab, religious and secular, and political and spiritual.

Florence
A city-size shrine to the Renaissance, Florence offers frescoes, sculptures, churches, palaces, and other monuments from the richest cultural flowering the world has known. Names from its dazzling historical past—Dante, Michelangelo, Galileo, Machiavelli—are some of the most resonant of the medieval age. But to see the Tuscan capital simply as Europe’s preeminent city of art would be to ignore not only its role as a dynamic and cosmopolitan metropolis, but also to overlook its more unsung charms—Italy’s most visited gardens (and its best ice-cream parlor), idyllic strolls on balmy summer evenings, a broad range of specialty shopping, sweeping views over majestic cityscapes, eating experiences that range from historic cafés to the country’s most highly rated restaurants, and the kind of seductive and romantic pleasures that somehow only Italy knows how to provide.

Dublin
In the last 20 years, the Republic of Ireland’s capital city has transformed itself from a quiet, economically depressed, old-fashioned town into a modern, thriving, affluent, and youthful (around 35 percent of the city’s million-plus people are under the age of 25) European city. Ancient pubs, lively nightclubs, hundreds of live music venues, and elegant restaurants share rain-soaked sod with hundreds of years of troubled, painful, and fascinating history carved into stone. The Liffey River divides the city into two distinct areas, both of which have seen an upswing in recent years. But as Joyce, Yeats, Swift, and their modern counterparts have eloquently demonstrated, every corner pub, emerald green, and Georgian square of Ireland’s largest city holds a story waiting to be shared.

Dubai
From sleepy trading port to global gateway in 25 years, the Middle East metropolis of Dubai has sprung up out of the desert sands. Once centered on bustling Dubai Creek, from where old dhows (boats) still sail to Iran, Dubai now sprawls south toward the United Arab Emirates’ capital, Abu Dhabi. While oil revenues fueled its early development, now trade and tourism power this city-state’s phenomenal growth rate. Travelers come for sun, sand, shopping, and a touch of the exotic, and Dubai delivers. While it might not have the ancient sites of Cairo or Damascus, Dubai just gets on with making history as one of the fastest growing cities in the world.

Delhi
With one foot deeply grounded in time-revered traditions and the other dipping more than just a few toes in the dotcom domain, Delhi embraces diversity with verve and gritty gumption. Modern Delhi has only been India’s capital since 1931, but thanks to its location—a strategic gateway city—it has long played a critical role in shaping the subcontinent’s history. Today, Delhi is one of India’s most multifaceted cities, with the downtown swish restaurants and chichi boutiques serving as a stark contrast to the old city’s medieval-flavored bazaars and historic masterpieces like the Red Fort and Jama Masjid.

Chicago
Poet Carl Sandburg immortalized Chicago as the “City of the Big Shoulders,” paying tribute to Chicago’s formative brawn. The self-made, industrious town rebuilt after a devastating 1871 fire, nurturing new styles of architecture and distinct flare for innovation. A green apron of lakefront parks buffers the city’s 29 miles (47 kilometers) of Lake Michigan shoreline from which 77 neighborhoods unfurl westward spanning the downtown Loop, the elegant Gold Coast, the bohemian Wicker Park, and deep ethnic pockets such as Chinatown. The combination of grit and grandeur here is somehow purely American. Loving Chicago, said author Nelson Algren, is “like loving a woman with a broken nose, you may well find lovelier lovelies. But never a lovely so real.”

Cape Town
What’s not to love about Cape Town? From iconic Table Mountain, several hundred million years in the making, to the hip watering holes of Camps Bay, South Africa’s “Mother City” is the brightest light in the reborn rainbow nation. Inspirational landscape, sugary sand beaches, centuries old vineyards, and colonial mansions, plus a host of adrenaline-pumping outdoor activities are among Cape Town’s many blessings. Factor in a colorful creative vibe and a lively social scene—manifesting itself in outstanding places to stay, eat, shop, and party—and you’ll soon realize why the city is South Africa's favorite playground.

Buenos Aires is often called the “Paris of South America,” for its soaring architecture and rich European heritage. But the city and its people, known as porteños, are a study in contrasts: European sensibilities and Latin American passion; wide boulevards and cobblestone alleys; steamy tango and romping rock and roll; sidewalk cafés and soccer fanatics; bejeweled ladies draped in fur coats and children rummaging through garbage for cardboard scraps. Buenos Aires, which sprawls over 78 square miles (202 square kilometers) and has a population of about three million, is a patchwork of distinct, fascinating communities, from the frenetic downtown and working-class tanguero neighborhoods such as La Boca and San Telmo, to wealthy districts such as Recoleta and trendy Palermo, to middle-class barrios such as Belgrano and Caballito.

Budapest—a city of thermal baths, cafés, striking turn-of-the-century architecture, and most of all, a city of the Danube, “whose gentle waves,” according to the great Hungarian poet Attila József, “embrace past, present, and future.” Straddling the wide river, which separates hilly Buda from level Pest, the Hungarian capital offers one of the most striking metropolitan panoramas in Europe. Budapest is a city of music, from the classics of Bartók and Kodály to the contemporary fusion of folk, klezmer, jazz, and Gypsy sounds. Long hidden behind the Iron Curtain, Budapest is rightfully regaining its reputation as one of the most vibrant capitals of central Europe.

Boston
Here’s a fresh observation: Boston is on the water. Who knew? For decades, ugly elevated highways crisscrossed the waterfront, blighting downtown. It took about 15 years and nearly $15 billion to put those highways underground in a sometimes controversial project known locally as “the Big Dig,” but Boston has reclaimed its status as a great port city with new parks, walkways, freshly renovated restaurants, newly built hotels, and a sense of excitement that has energized the whole city. New downtown attractions like the Rose Fitzgerald Kennedy Greenway (on the site of what used to be Interstate 93) and the Harborwalk (a walking and running path that lines Boston’s waterfront) are spawning an explosion in great hotels, cafés, and hot spots.

Berlin
Berlin has had a more wrenching history than most cities on Earth. It’s been ravaged by war, enslaved by fascism, bisected during the Cold War, and rejoined at the fall of the Wall. Out of such chaos has grown a city that’s adaptable in the extreme. Its waves of immigrants, expats, and creatives ensure that tolerance is its greatest value. Nightlife and partying here are akin to religious rites, and new trends emerge 24/7. But Berlin is also a place of incredible beauty in its forests, rivers, and historical sites. Culture blossoms everywhere, and dining is an international smorgasbord. You’ll find any version of Berlin you envision and, in the process, perhaps find a new version of yourself.

Barcelona
Long pegged as a mere “smokestack city,”Barcelona has come into its own since the 1992 Olympics, and today is one of the liveliest tourist destinations in Europe. Cradled between the Mediterranean and the Serra de Collserola hills, Spain’s second largest metropolis arguably eclipses Madrid as a showcase for the arts, music, and cutting-edge design. A morning’s walk can take you from the original Roman settlement, much of it still intact under the narrow streets of the medieval Barri Gòtic, to the palaces and churches of the city’s 12th- and 13th-century golden age and on to the 19th-century L’Eixample neighborhood, where every avenue seems to be lined with flights of architectural fancy in stained glass and wrought iron, ornamental brick, and ceramic tile.