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.