Day 1 Venice, Italy

Venice is a city unlike any other. No matter how often you've seen it in photos and films, the real thing is more dreamlike than you could imagine. With canals where streets should be, water shimmers everywhere. The fabulous palaces and churches reflect centuries of history in what was a wealthy trading center between Europe and the Orient. Getting lost in the narrow alleyways is a quintessential part of exploring Venice, but at some point you'll almost surely end up in Piazza San Marco, where tourists and locals congregate for a coffee or an aperitif.

Day 3 Corfu, Greece

Corfu town today is a vivid tapestry of cultures—a sophisticated weave, where charm, history, and natural beauty blend. Located about midway along the island's east coast, this spectacularly lively capital is the cultural heart of Corfu and has a remarkable historic center that UNESCO designated as a World Heritage Site in 2007. All ships and planes dock or land near Corfu town, which occupies a small peninsula jutting into the Ionian Sea.Whether arriving by ferry from mainland Greece or Italy, from another island, or directly by plane, catch your breath by first relaxing with a coffee or a gelato in Corfu town's shaded Liston Arcade, then stroll the narrow lanes of its pedestrians-only quarter. For an overview of the immediate area, and a quick tour of Mon Repos palace, hop on the little tourist train that runs from May to September. Corfu town has a different feel at night, so book a table at one of its famed tavernas to savor the island's unique cuisine.The best way to get around Corfu town is on foot. The town is small enough so that you can easily walk to every sight. There are local buses, but they do not thread their way into the streets (many now car-free) of the historic center. If you are arriving by ferry or plane, it's best to take a taxi to your hotel. Expect to pay about €10 from the airport or ferry terminal to a hotel in Corfu town. If there are no taxis waiting, you can call for one.

Day 5 Siracuse, Sicily, Italy

Siracusa, known to English speakers as Syracuse, is a wonder to behold. One of the great ancient capitals of Western civilization, the city was founded in 734 BC by Greek colonists from Corinth and soon grew to rival, and even surpass, Athens in splendor and power. It became the largest, wealthiest city-state in the West and a bulwark of Greek civilization. Although Siracusa lived under tyranny, rulers such as Dionysius filled their courts with Greeks of the highest cultural stature—among them the playwrights Aeschylus and Euripides, and the philosopher Plato. The Athenians, who didn't welcome Siracusa's rise, set out to conquer Sicily, but the natives outsmarted them in what was one of the greatest military campaigns in ancient history (413 BC). The city continued to prosper until it was conquered two centuries later by the Romans.Present-day Siracusa still has some of the finest examples of Baroque art and architecture; dramatic Greek and Roman ruins; and a Duomo that's the stuff of legend—a microcosm of the city's entire history in one building. The modern city also has a wonderful, lively, Baroque old town worthy of extensive exploration, as well as pleasant piazzas, outdoor cafés and bars, and a wide assortment of excellent seafood. There are essentially two areas to explore in Siracusa: the Parco Archeologico (Archaeological Zone), on the mainland; and the island of Ortygia, the ancient city first inhabited by the Greeks, which juts out into the Ionian Sea and is connected to the mainland by two small bridges. Ortygia is becoming increasingly popular with tourists, and is starting to lose its old-fashioned charm in favor of modern boutiques.Siracusa's old nucleus of Ortygia, a compact area, is a pleasure to amble around without getting unduly tired. In contrast, mainland Siracusa is a grid of wider avenues. At the northern end of Corso Gelone, above Viale Paolo Orsi, the orderly grid gives way to the ancient quarter of Neapolis, where the sprawling Parco Archeologico is accessible from Viale Teracati (an extension of Corso Gelone). East of Viale Teracati, about a 10-minute walk from the Parco Archeologico, the district of Tyche holds the archaeological museum and the church and catacombs of San Giovanni, both off Viale Teocrito (drive or take a taxi or city bus from Ortygia). Coming from the train station, it's a 15-minute trudge to Ortygia along Via Francesco Crispi and Corso Umberto. If you're not up for that, take one of the free electric buses leaving every 10 minutes from the bus station around the corner.

Day 6 Palermo, Italy

Once the intellectual capital of southern Europe, Palermo has always been at the crossroads of civilization. Favorably situated on a crescent-shaped bay at the foot of Monte Pellegrino, it has attracted almost every culture touching the Mediterranean world. To Palermo's credit, it has absorbed these diverse cultures into a unique personality that is at once Arab and Christian, Byzantine and Roman, Norman and Italian. The city's heritage encompasses all of Sicily's varied ages, but its distinctive aspect is its Arab-Norman identity, an improbable marriage that, mixed in with Byzantine and Jewish elements, created some resplendent works of art. No less noteworthy than the architecture is Palermo's chaotic vitality, on display at some of Italy's most vibrant outdoor markets, public squares, street bazaars, and food vendors, and above all in its grand climax of Italy's most spectacular passeggiata (the leisurely social stroll along the principal thoroughfare).

Day 8 Valencia, Spain

Valencia, Spain's third-largest municipality, is a proud city with a thriving nightlife and restaurant scene, quality museums, and spectacular contemporary architecture, juxtaposed with a thoroughly charming historic quarter, making it a popular destination year in year out. During the Civil War, it was the last seat of the Republican Loyalist government (1935–36), holding out against Franco's National forces until the country fell to 40 years of dictatorship. Today it represents the essence of contemporary Spain—daring design and architecture along with experimental cuisine—but remains deeply conservative and proud of its traditions. Though it faces the Mediterranean, Valencia's history and geography have been defined most significantly by the River Turia and the fertile huerta that surrounds it.The city has been fiercely contested ever since it was founded by the Greeks. El Cid captured Valencia from the Moors in 1094 and won his strangest victory here in 1099: he died in the battle, but his corpse was strapped into his saddle and so frightened the besieging Moors that it caused their complete defeat. In 1102 his widow, Jimena, was forced to return the city to Moorish rule; Jaume I finally drove them out in 1238. Modern Valencia was best known for its frequent disastrous floods until the River Turia was diverted to the south in the late 1950s. Since then the city has been on a steady course of urban beautification. The lovely bridges that once spanned the Turia look equally graceful spanning a wandering municipal park, and the spectacularly futuristic Ciutat de les Arts i les Ciències (City of Arts and Sciences), most of it designed by Valencia-born architect Santiago Calatrava, has at last created an exciting architectural link between this river town and the Mediterranean. If you're in Valencia, an excursion to Albufera Nature Park is a worthwhile day trip.

Day 11 Santa Cruz de Tenerife, Spain

The largest of the Canary Islands, Tenerife is a beautiful and scenic island which enjoys year-round sunshine and is dominated by Mount Teide. The mountain range runs through the centre of the island, with fertile valleys on the northern side. In the central part of the range is the gigantic natural crater of the Cañadas del Teide, about 14 miles in diameter. Santa Cruz, the island's pretty capital, was originally a small fishing village but has now grown into a modern city, and also contains 16th-century civic buildings and ornate private mansions. Near the pier is the Santa Cruz Palmetum, a Botanical Garden covering an area of 29 acres, specialising in palms.

Day 17 Recife, Brazil

This vibrant metropolis has a spirit that's halfway between that of the modern cities of Brazil's South and of the traditional northeastern centers. It offers both insight on the past and a window to the future.It was in Pernambuco State, formerly a captaincy, that the most violent battles between the Dutch and the Portuguese took place. Under the Portuguese, the capital city was the nearby community of Olinda. But beginning in 1637 and during the Dutch turn at the reins (under the powerful count Maurício de Nassau), both Olinda and Recife were greatly developed.The city has beautiful buildings alongside the rivers that remind many visitors of Europe. Unfortunately, huge swathes of 19th-century buildings were razed to make way for modern structures. As a result, the center of the city has pockets of neocolonial splendor surrounded by gap-toothed modern giants. Today Recife is a leader in health care and has benefited from significant government investment in recent years, resulting in a boom in infrastructure and construction industries. It's also Brazil's third-largest gastronomic center—it's almost impossible to get a bad meal here.Recife is built around three rivers and connected by 49 bridges. Its name comes from the recifes (reefs) that line the coast. Because of this unique location, water and light often lend the city interesting textures. In the morning, when the tide recedes from Boa Viagem Beach, the rocks of the reefs slowly reappear. Pools of water are formed, fish flap around beachgoers, and the rock formations dry into odd colors. And if the light is just right on the Rio Capibaribe, the ancient buildings of Recife Antigo (Old Recife) are reflected off the river's surface in a watercolor display.

Day 20 Buzios, Brazil

Around two hours from Rio de Janeiro, Búzios is a string of beautiful beaches on an 8-km-long (5-mile-long) peninsula. It was the quintessential sleepy fishing village until the 1960s, when the French actress Brigitte Bardot holidayed here to escape the paparazzi and the place almost instantly transformed into a vacation sensation. Búzios has something for everyone. Some hotels cater specifically to families and provide plenty of activities and around-the-clock child care. Many have spa facilities, and some specialize in weeklong retreats. For outdoor enthusiasts, Búzios offers surfing, windsurfing, kitesurfing, diving, hiking, and mountain biking, as well as leisurely rounds of golf.

Day 21 Rio de Janeiro, Brazil

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.