On one of the best stretches of the Mediterranean, this classic luxury destination is one of the most sought-after addresses in the world. With all the high-rise towers you have to look hard to find the Belle Époque grace of yesteryear. But if you head to the town's great 1864 landmark Hôtel de Paris—still a veritable crossroads of the buffed and befurred Euro-gentry—or enjoy a grand bouffe at its famous Louis XV restaurant, or attend the opera, or visit the ballrooms of the casino, you may still be able to conjure up Monaco's elegant past. Prince Albert II, a political science graduate from Amherst College, traces his ancestry to Otto Canella, who was born in 1070. The Grimaldi dynasty began with Otto's great-great-great-grandson, Francesco Grimaldi, also known as Frank the Rogue. Expelled from Genoa, Frank and his cronies disguised themselves as monks and in 1297 seized the fortified medieval town known today as Le Rocher (the Rock). Except for a short break under Napoléon, the Grimaldis have been here ever since, which makes them the oldest reigning family in Europe.

In the 1850s a Grimaldi named Charles III made a decision that turned the Rock into a giant blue chip. Needing revenue but not wanting to impose additional taxes on his subjects, he contracted with a company to open a gambling facility. The first spin of the roulette wheel was on December 14, 1856. There was no easy way to reach Monaco then—no carriage roads or railroads—so no one came. Between March 15 and March 20, 1857, one person entered the casino—and won two francs. In 1868, however, the railroad reached Monaco, and it was filled with Englishmen who came to escape the London fog. The effects were immediate. Profits were so great that Charles eventually abolished all direct taxes. Almost overnight, a threadbare principality became an elegant watering hole for European society. Dukes (and their mistresses) and duchesses (and their gigolos) danced and dined their way through a world of spinning roulette wheels and bubbling champagne—preening themselves for nights at the opera, where such artists as Vaslav Nijinsky, Sarah Bernhardt, and Enrico Caruso came to perform. Along with the tax system, its sensational position on a broad, steep peninsula that bulges into the Mediterranean—its harbor sparkling with luxury cruisers, its posh mansions angling awnings toward the nearly perpetual sun—continues to draw the rich and famous. One of the latest French celebrities to declare himself "Monégasque," thus giving up his French passport, is superchef Alain Ducasse, who said that he made the choice out of affection for Monaco rather than tax reasons.

Pleasure boats vie with luxury cruisers in their brash beauty and Titanic scale, and teams of handsome young men—themselves dyed blond and tanned to match—scour and polish every gleaming surface. As you might expect, all this glitz doesn't come cheap. Eating is expensive, and even the most modest hotels cost more here than in nearby Nice or Menton. As for taxis, they don't even have meters so you are completely at the driver's mercy (with prices skyrocketing during events such as the Grand Prix). For the frugal, Monaco is the ultimate day-trip, although parking is as coveted as a room with a view. At the very least you can afford a coffee at Starbucks. The harbor district, known as La Condamine, connects the new quarter, officially known as Monte Carlo with Monaco-Ville (or Le Rocher), a medieval town on the Rock, topped by the palace, the cathedral, and the Oceanography Museum. Have no fear that you'll need to climb countless steps to get to Monaco-Ville, as there are plenty of elevators and escalators climbing the steep cliffs. But shuttling between the lovely casino grounds of Monte Carlo and Old Monaco, separated by a vast port, is a daunting proposition for ordinary mortals without wings, so hop on the No. 1 bus from Saint Roman, or No. 2 from the Jardin Exotique - Both stop at Place du Casino and come up to Monaco Ville.

One of the most photographed villages along the coast, with a decidedly romantic and affluent aura, Portofino has long been a popular destination for the rich and famous. Once an ancient Roman colony and taken by the Republic of Genoa in 1229, it’s also been ruled by the French, English, Spanish, and Austrians, as well as by marauding bands of 16th-century pirates. Elite British tourists first flocked to the lush harbor in the mid-1800s. Some of Europe's wealthiest drop anchor in Portofino in summer, but they stay out of sight by day, appearing in the evening after buses and boats have carried off the day-trippers.

There's not actually much to do in Portofino other than stroll around the wee harbor, see the castle, walk to Punta del Capo, browse at the pricey boutiques, and sip a coffee while people-watching. However, weaving through picture-perfect cliffside gardens and gazing at yachts framed by the sapphire Ligurian Sea and the cliffs of Santa Margherita can make for quite a relaxing afternoon. There are also several tame, photo-friendly hikes into the hills to nearby villages.

Unless you're traveling on a deluxe budget, you may want to stay in Camogli or Santa Margherita Ligure rather than at one of Portofino's few very expensive hotels. Restaurants and cafés are good but also pricey (don't expect to have a beer here for much under €10).

Livorno is a gritty city with a long and interesting history. In the early Middle Ages it alternately belonged to Pisa and Genoa. In 1421 Florence, seeking access to the sea, bought it. Cosimo I (1519–74) started construction of the harbor in 1571, putting Livorno on the map. After Ferdinando I de' Medici (1549–1609) proclaimed Livorno a free city, it became a haven for people suffering from religious persecution; Roman Catholics from England and Jews and Moors from Spain and Portugal, among others, settled here. The Quattro Mori (Four Moors), also known as the Monument to Ferdinando I, commemorates this. (The statue of Ferdinando I dates from 1595, the bronze Moors by Pietro Tacca from the 1620s.)

In the following centuries, and particularly in the 18th, Livorno boomed as a port. In the 19th century the town drew a host of famous Britons passing through on their grand tours. Its prominence continued up to World War II, when it was heavily bombed. Much of the town's architecture, therefore, postdates the war, and it's somewhat difficult to imagine what it might have looked like before. Livorno has recovered from the war, however, as it's become a huge point of departure for container ships, as well as the only spot in Tuscany for cruise ships to dock for the day.

Most of Livorno's artistic treasures date from the 17th century and aren't all that interesting unless you dote on obscure baroque artists. Livorno's most famous native artist, Amedeo Modigliani (1884–1920), was of much more recent vintage. Sadly, there's no notable work by him in his hometown.

There may not be much in the way of art, but it's still worth strolling around the city. The Mercato Nuovo, which has been around since 1894, sells all sorts of fruits, vegetables, grains, meat, and fish. Outdoor markets nearby are also chock-full of local color. The presence of Camp Darby, an American military base just outside town, accounts for the availability of many American products.

If you have time, Livorno is worth a stop for lunch or dinner at the very least.

Days at sea are the perfect opportunity to relax, unwind and catch up with what you’ve been meaning to do. So whether that is going to the gym, visiting the spa, whale watching, catching up on your reading or simply topping up your tan, these blue sea days are the perfect balance to busy days spent exploring shore side.

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).

Naples, in the Campania region, is Italy's third largest city. Its claim to fame is the spectacular location along one of the world's most splendid bays, backed by the perfect cone of Mount Vesuvius. In addition to its beautiful setting, Naples' surprises with other outstanding attractions such as the Royal Palace, San Carlos Opera House, the impressive National Archaeological Museum and the Castel Nuovo, dating from the 13th-century. The city's central area is best explored on foot. Chaotic traffic conditions make driving around the city a very frustrating experience. Naples provides a convenient starting point for trips to such favored destinations as Pompeii, Herculaneum and Mount Vesuvius. The Isle of Capri can be reached via a 45-minute hydrofoil service. The region of Campania was home to Greeks settlers some 300 years before Rome was founded. Pompeii, too, was a Greek town before being conquered by the Romans during the 5th century BC. It was under the Romans that Pompeii flourished and grew prosperous. When Mount Vesuvius erupted in 79 AD, the population of 20,000 was wiped out, but dozens of buildings were preserved under layers of cinder more than 20 feet deep. The most important finds from Pompeii are displayed in Naples' National Archaeological Museum. A visit here will no doubt enhance a visit to ancient Pompeii.

Italy's vibrant capital lives in the present, but no other city on earth evokes its past so powerfully. For over 2,500 years, emperors, popes, artists, and common citizens have left their mark here. Archaeological remains from ancient Rome, art-stuffed churches, and the treasures of Vatican City vie for your attention, but Rome is also a wonderful place to practice the Italian-perfected il dolce far niente, the sweet art of idleness. Your most memorable experiences may include sitting at a caffè in the Campo de' Fiori or strolling in a beguiling piazza.