Brazil, Spain, Italy

Welcome to the Cidade Maravilhosa, or the Marvelous City, as Rio is known in Brazil. Synonymous with the girl from Ipanema, the dramatic views from Christ the Redeemer atop Corcovado mountain, and fabulously flamboyant Carnival celebrations, Rio is a city of stunning architecture, abundant museums, and marvelous food. Rio is also home to 23 beaches, an almost continuous 73-km (45-mile) ribbon of sand.As you leave the airport and head to Rio's beautiful Zona Sul (the touristic South Zone), you'll drive for about 40 minutes on a highway from where you'll begin to get a sense of the dramatic contrast between beautiful landscape and devastating poverty. In this teeming metropolis of 12 million people (6.2 million of whom live in Rio proper), the very rich and the very poor live in uneasy proximity. You'll drive past seemingly endless cinder-block favela, but by the time you reach Copacabana's breezy, sunny Avenida Atlântica—flanked on one side by white beach and azure sea and on the other by condominiums and hotels—your heart will leap with expectation as you begin to recognize the postcard-famous sights. Now you're truly in Rio, where cariocas (Rio residents) and tourists live life to its fullest.Enthusiasm is contagious in Rio. Prepare to have your senses engaged and your inhibitions untied. Rio seduces with a host of images: the joyous bustle of vendors at Sunday's Feira Hippie (Hippie Fair); the tipsy babble at sidewalk cafés as patrons sip their last glass of icy beer under the stars; the blanket of lights beneath the Pão de Açúcar (Sugarloaf Mountain); the bikers, joggers, strollers, and power walkers who parade along the beach each morning. Borrow the carioca spirit for your stay; you may find yourself reluctant to give it back.

Maceió, city, capital of Alagoas estado (state), northeastern Brazil. It is situated below low bluffs on a level strip of land between the Atlantic Ocean and the Norte (or Mundaú) Lagoon, a shallow body of water extending inward for several miles. Formerly called Macayo, the city dates from 1815, when a small settlement there was made a villa. In 1839 it became capital of Alagoas (then a provincia) and was given city status.

Perhaps the prettiest of the Canary Islands, Gran Canaria is an almost circular isle with the peak of Pozo de Las Nieves, its highest point, at the centre. With a wealth of natural beauty and all the exciting attractions of city life in the capital, the island offers the best of both worlds. You will no doubt wish to see the sights of the capital’s old quarter, which dates back to the 15th century and encompassses the Vegueta and Triana districts, and wherever you go you can enjoy the glorious subtropical climate, perfect for growing exotic palms and fruits.

The provincial capital of the Valencian Community serves as a gateway to the huge influx of tourists that flock to the Costa Blanca resorts every year. Alicante is popular with holidaymakers who arrive for the warm, Mediterranean climate and seemingly endless golden beaches. However, there is much more to this city than sand and sun. With a picturesque waterfront, a hugely impressive castle, buzzing nightlife and a rich, complex history, Alicante is a fascinating destination all year round.

If you look north of the cathedral (La Seu, or the seat of the bishopric, to Mallorcans) on a map of the city of Palma, you can see around the Plaça Santa Eulàlia a jumble of tiny streets that made up the earliest settlement. Farther out, a ring of wide boulevards traces the fortifications built by the Moors to defend the larger city that emerged by the 12th century. The zigzags mark the bastions that jutted out at regular intervals. By the end of the 19th century, most of the walls had been demolished; the only place where you can still see the massive defenses is at Ses Voltes, along the seafront west of the cathedral.A torrent (streambed) used to run through the middle of the old city, dry for most of the year but often a raging flood in the rainy season. In the 17th century it was diverted to the east, along the moat that ran outside the city walls. Two of Palma's main arteries, La Rambla and the Passeig d'es Born, now follow the stream's natural course. The traditional evening paseo (promenade) takes place on the Born.If you come to Palma by car, park in the garage beneath the Parc de la Mar (the ramp is just off the highway from the airport, as you reach the cathedral) and stroll along the park. Beside it run the huge bastions guarding the Almudaina Palace; the cathedral, golden and massive, rises beyond. Where you exit the garage, there's a ceramic mural by the late Catalan artist and Mallorca resident Joan Miró, facing the cathedral across the pool that runs the length of the park.If you begin early enough, a walk along the ramparts at Ses Voltes from the mirador beside the cathedral is spectacular. The first rays of the sun turn the upper pinnacles of La Seu bright gold and then begin to work their way down the sandstone walls. From the Parc de la Mar, follow Avinguda Antoni Maura past the steps to the palace. Just below the Plaça de la Reina, where the Passeig d'es Born begins, turn left on Carrer de la Boteria into the Plaça de la Llotja (if the Llotja itself is open, don't miss a chance to visit—it's the Mediterranean's finest Gothic-style civic building). From there stroll through the Plaça Drassana to the Museu d'Es Baluard, at the end of Carrer Sant Pere. Retrace your steps to Avinguda Antoni Maura. Walk up the Passeig d'es Born to Plaça Joan Carles I, then right on Avenida de La Unió.

The infinite variety of street life, the nooks and crannies of the medieval Barri Gòtic, the ceramic tile and stained glass of Art Nouveau facades, the art and music, the throb of street life, the food (ah, the food!)—one way or another, Barcelona will find a way to get your full attention. The capital of Catalonia is a banquet for the senses, with its beguiling mix of ancient and modern architecture, tempting cafés and markets, and sun-drenched Mediterranean beaches. A stroll along La Rambla and through waterfront Barceloneta, as well as a tour of Gaudí's majestic Sagrada Famíliaand his other unique creations, are part of a visit to Spain's second-largest city. Modern art museums and chic shops call for attention, too. Barcelona's vibe stays lively well into the night, when you can linger over regional wine and cuisine at buzzing tapas bars.

Since being designated a European Capital of Culture for 2013, with an estimated €660 million of funding in the bargain, Marseille has been in the throes of an extraordinary transformation, with no fewer than five major new arts centers, a beautifully refurbished port, revitalized neighborhoods, and a slew of new shops and restaurants. Once the underdog, this time-burnished city is now welcoming an influx of weekend tourists who have colonized entire neighborhoods and transformed them into elegant pieds-à-terre (or should we say, mer). The second-largest city in France, Marseille is one of Europe's most vibrant destinations. Feisty and fond of broad gestures, it is also as complicated and as cosmopolitan now as it was when a band of Phoenician Greeks first sailed into the harbor that is today's Vieux Port in 600 BC. Legend has it that on that same day a local chieftain's daughter, Gyptis, needed to choose a husband, and her wandering eyes settled on the Greeks' handsome commander Protis. Her dowry brought land near the mouth of the Rhône, where the Greeks founded Massalia, the most important Continental shipping port in antiquity. The port flourished for some 500 years as a typical Greek city, enjoying the full flush of classical culture, its gods, its democratic political system, its sports and theater, and its naval prowess. Caesar changed all that, besieging the city in 49 BC and seizing most of its colonies. In 1214 Marseille was seized again, this time by Charles d'Anjou, and was later annexed to France by Henri IV in 1481, but it was not until Louis XIV took the throne that the biggest transformations of the port began; he pulled down the city walls in 1666 and expanded the port to the Rive Neuve (New Riverbank). The city was devastated by plague in 1720, losing more than half its population. By the time of the Revolution, Marseille was on the rebound once again, with industries of soap manufacturing and oil processing flourishing, encouraging a wave of immigration from Provence and Italy. With the opening of the Suez Canal in 1869, Marseille became the greatest boomtown in 19th-century Europe. With a large influx of immigrants from areas as exotic as Tangiers, the city quickly acquired the multicultural population it maintains to this day.