Day 1 Sydney, New South Wales, Australia

Sydney belongs to the exclusive club of cities that generate excitement. At the end of a marathon flight there's renewed vitality in the cabin as the plane circles the city, where thousands of yachts are suspended on the dark water and the sails of the Opera House glisten in the distance. Blessed with dazzling beaches and a sunny climate, Sydney is among the most beautiful cities on the planet.With 4.6 million people, Sydney is the biggest and most cosmopolitan city in Australia. A wave of immigration from the 1950s has seen the Anglo-Irish immigrants who made up the city's original population joined by Italians, Greeks, Turks, Lebanese, Chinese, Vietnamese, Thais, and Indonesians. This intermingling has created a cultural vibrancy and energy—and a culinary repertoire—that was missing only a generation ago.Sydneysiders embrace their harbor with a passion. Indented with numerous bays and beaches, Sydney Harbour is the presiding icon for the city, and urban Australia. Captain Arthur Phillip, commander of the 11-ship First Fleet, wrote in his diary when he first set eyes on the harbor on January 26, 1788: "We had the satisfaction of finding the finest harbor in the world."Although a visit to Sydney is an essential part of an Australian experience, the city is no more representative of Australia than Los Angeles is of the United States. Sydney has joined the ranks of the great cities whose characters are essentially international. What Sydney offers is style, sophistication, and great looks—an exhilarating prelude to the continent at its back door.

Day 4 Nouméa, New Caledonia

With its elegant urban infrastructure in a stunning natural setting, Noumea is a truly unique island and part of the New Caledonia archipelago. Noumea started as a penal colony, but has since evolved to a lovely metropolis and today has almost two thirds of New Caledonia's population. While much of the archipelago of New Caledonia has a large percentage of Kanak people – the indigenous inhabitants who live in tribal areas across the country – Noumea is predominantly European with a strong French influence. The city's center and Place de Cocotiers, the main park, are located close to the harbor and several churches date back to the late 19th century. Other attractions include a world-class aquarium at Anse Vata, several long beaches to the south, and a noteworthy collection of Kanak and South Pacific objects at the Museum of New Caledonia. The architectural gem of the city is the Tjibaou Cultural Center, the structure of which resembles sails, or the roofs of Kanak houses hidden behind mangroves.

Day 6 Luganville, Vanuatu

Day 10 Pago Pago, American Samoa

American Samoa is a tropical paradise, located in the Pacific Ocean and home to some of the world's most unique flora and fauna. Pago Pago is the main harbour and village of Tutuila island. It is considered the capital of the territory and is the entry point for visitors exploring the picturesque volcanic islands.

Day 16 Honolulu, Hawaii, United States

Capital of Hawaii, and a popular tourist destination, Honolulu is known for surfing and water sports. However, there's more to the city than surfing; with museums, the only royal palace in the country, and a mall, there's bound to be something of interest for any visitor.

Day 17 Hilo, Hawaii, United States

Day 23 Los Angeles, California, United States

Home of the famous Hollywood sign and Walk of Fame, Los Angeles is the place to visit for anyone interested in film and television and hoping to get a glimpse at some famous actors and artists. Stroll down the Walk and enjoy the glamorous atmosphere and famous surroundings, or take a break on the Santa Monica pier and watch the sun set on the sea.

Day 26 Cabo San Lucas, Mexico

Cabo San Lucas, a resort city on the southern tip of Mexico's Baja California peninsula, is known for its beaches, water-based activities and nightlife. Playa El Médano is Cabo's main beach, with outdoor restaurants and numerous bars. Past the marina is Land's End promontory, site of Playa del Amor (Lover's Beach) and El Arco, a natural archway in the seacliffs.

Day 30 Puntarenas, Costa Rica

This town is not on the Nicoya Peninsula, but rather on Costa Rica's mainland. It is best known as a cruise-ship port and launching pad for ferries heading southeast to the coast of the Nicoya Peninsula and for cruises sailing out on the Gulf of Nicoya. Puntarenas is also a major fishing port with a lively fish market. The town's reputation suffers from the unimpressive parts you see from your car as you roll through town on the way to the ferry dock. But the town has a lot of character off the main drag, thanks to its illustrious past as an affluent port town and principal vacation spot for San José's wealthy, who arrived by train in the last century. Once the port was moved and roads opened to other beaches, Puntarenas's economy crashed, but it's making a comeback. Sitting on a narrow spit of sand—punta de arenas literally means "point of sand"—that protrudes into the Gulf of Nicoya, the town boasts a beautifully groomed, wide Blue Flag beach with views of the Nicoya Peninsula and spectacular sunsets, along with a public swimming pool, the San Lucas Beach Club, and a marine-life museum. Ticos arrive by bus and car to enjoy the beach and stroll the Paseo de los Turistas, a beachfront promenade lined with tree-shaded concrete benches and seafood restaurants. Crowds of locals, called porteños, cruise by on bicycles, the town's most popular form of transport.

Day 34 Ocho Rios, Jamaica

Day 37 Road Town, Tortola, British Virgin Islands

Day 38 Philipsburg, Sint Maarten (Dutch part)

The capital of Dutch St. Maarten stretches about a mile (1½ km) along an isthmus between Great Bay and the Salt Pond and has five parallel streets. Most of the village's dozens of shops and restaurants are on Front Street, narrow and cobblestone, closest to Great Bay. It's generally congested when cruise ships are in port, because of its many duty-free shops and several casinos. Little lanes called steegjes connect Front Street with Back Street, which has fewer shops and considerably less congestion. Along the beach is a ½-mile-long (1-km-long) boardwalk with restaurants and several Wi-Fi hot spots.Wathey Square (pronounced watty) is in the heart of the village. Directly across from the square are the town hall and the courthouse, in a striking white building with cupola. The structure was built in 1793 and has served as the commander's home, a fire station, a jail, and a post office. The streets surrounding the square are lined with hotels, duty-free shops, restaurants, and cafés. The Captain Hodge Pier, just off the square, is a good spot to view Great Bay and the beach that stretches alongside.

Day 45 Las Palmas de Gran Canaria, Spain

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.

Day 48 Palma de Mallorca, Spain

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.

Day 50 Naples, Italy

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.

Day 51 Civitavecchia, Italy

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.