Paris, France

Long considered the paragon of style, Paris is the most glamorous city in Europe. It is at once deeply traditional – a village-like metropolis whose inhabitants continue to be notorious for their hauteur – and famously cosmopolitan. While such contradictions and contrasts may be the reality of any city, they are the makings of Paris: consider the tiny lanes and alleyways of the Quartier Latin or Montmartre against the monumental vistas from the Louvre to La Défense; the multiplicity of street markets and old-fashioned pedestrian arcades against the giant underground commercial complexes of Montparnasse and Les Halles; or the aristocratic wealth of the grand quarters against the vibrant chaos of the poorer districts.

At times, Paris can feel inhumanly magnificent, the arrogance of its monuments encompassing the chilly pomp of the Panthéon, the industrial chic of the Eiffel Tower and the almost spiritual glasswork of the Louvre pyramid. Yet it also operates on a very human scale, with exquisite, secretive little nooks tucked away from the Grands Boulevards and very definite little communities revolving around games of boules and the local boulangerie and café. And even as Paris's culture is transformed by its large immigrant and gay populations, even as extravagant new buildings are commissioned and erected, many of the city's streets, cafés and restaurants remain remarkably, defiantly unchanged.

San Juan, Puerto Rico

Founded in 1521 by Ponce de León, the capital of Puerto Rico, San Juan, is the oldest city in US territory. Home to 1.6 million (more than a third of the island's citizens), it is also the heart of Puerto Rican tourism. What draws travellers here year-round are miles of smooth, clean beaches, a wide range of accommodation, fabulous restaurants and, of course, Old San Juan, whose beautifully restored historic sights surrounded by crashing turquoise surf are reason enough to make a trip to Puerto Rico.

Along with Old San Juan, resort-filled Condado is the most popular neighbourhood for visitors thanks to its excellent beachfront and fine boutiques, and these two sections of the capital share the highest concentration of restaurants and lodging options. There's also much to explore as the city extends to the south and east, including the beachfront neighbourhoods of Ocean Park and Isla Verde; up-and-coming Santurce with its numerous art galleries; the financial district of Hato Rey; and the college-town vibe in Rio Piedras.

Cape Town, South Africa

CAPE TOWN is southern Africa's most beautiful, most romantic and most visited city. Indeed, few urban centres anywhere can match its setting along the mountainous Cape Peninsula spine, which slides into the Atlantic Ocean. By far the most striking – and famous – of its sights is Table Mountain, frequently shrouded by clouds, and rearing up from the middle of the city.

More than a scenic backdrop, Table Mountain is the solid core of Cape Town, dividing the city into distinct zones with public gardens, wilderness, forests, hiking routes, vineyards and desirable residential areas trailing down its lower slopes. Standing on the tabletop, you can look north for a giddy view of the city centre, its docks lined with matchbox ships. Looking west, beyond the mountainous Twelve Apostles, the drop is sheer and your eye will sweep across Africa's priciest real estate, clinging to the slopes along the chilly but spectacularly beautiful Atlantic seaboard. Turning south, the mountainsides are forested and several historic vineyards and the marvellous Botanical Gardens creep up the lower slopes. Beyond the oak-lined suburbs of Newlands and Constantia lies the warmer False Bay seaboard, which curves around towards Cape Point. Finally, relegated to the grim industrial east, are the coloured townships and black ghettos, spluttering in winter under the smoky pall of coal fires – your stark introduction to Cape Town when driving in.

Shanghai, China

After forty years of stagnation, the great metropolis of SHANGHAI is currently undergoing one of the fastest economic expansions that the world has ever seen. While shops overflow and the skyline fills with skyscrapers, Shanghai now seems certain to recapture its position as East Asia's leading business city, a status it last held before World War II. And yet, for all the modernization Shanghai has retained deep links with its colonial past.

Shanghai is still known in the West for its infamous role as the base of European imperialism in mainland China – its decadence, illicit pleasures, racism, appalling social inequalities, and Mafia syndicates. The intervening fifty years have almost been forgotten, as though the period from when the Communists arrived and the foreigners moved out was an era in which nothing happened. To some extent this perception is actually true: for most of the Communist period into the early 1990s, the central government in Beijing deliberately ran Shanghai down, siphoning off its surplus to other parts of the country to the point where the city came to resemble a living museum, frozen in time since the 1940s, and housing the largest array of Art Deco architecture in the world.