To the first-time visitor, Palermo is a city of ever-changing character. An abundance of dusty museums, Arabian domes and flourishes of baroque splendor jostle with boisterous markets, chaotic traffic and oppressive summer heat. The Sicilian hotspot is a noisy, polluted, often dangerous, but always fascinating city. Don't miss marvels of Arab-Norman architecture, such as 12th-century Palazzo dei Normanni or San Giovanni degli Eremiti. Ask your hotel to arrange cabs and negotiate fares before setting off.

The Mediterranean's biggest island is separated from the mainland by the Strait of Messina. A mountainous spot, Sicily's coast and its small islands sit at the foot of volcanoes, including Etna, Stromboli and Vulcano. The Greeks, Romans, Normans and Catalans all left their mark on the island in the form of Byzantine palaces, Gothic castles and Baroque flourishes in capital Palermo. Most larger towns offer interesting museums, but Etna and the Hellenic temples in Agrigento offer particularly unique sights.

Potsdam was the residence of the Prussian kings and German Kaisers until 1918. It is the site of the parks and palaces of Sanssouci, the largest World Heritage Site in Germany. The city is now the capital of the German federal state of Brandenburg and a home to three public colleges and a major film production studio.

The people of Tamil Nadu consider providing food to others a service to humanity. Thus the service in the state capital, Chennai, is first-rate. Treat your senses to some of the richest South Indian flavours in traditional dishes like sambar, rasam, fish curry or kootu. And don't forget to have a cup of full-bodied Tamil coffee, enhanced with chicory—no visit is complete without it.

Blossoming bougainvilleas, crumbling cathedrals on leafy boulevards and 18th-century colonial buildings colour the former French colony of Pondy, which sits on the Bay of Bengal. But it's also unmistakably Indian, with colourful festivals throughout the year, several mosques and the Sri Aurobindo Ashram. Quiet beaches stretch north and south from town, good for swimming and sunrise strolls. Pondy is a popular weekend getaway destination from Chennai and is easy to navigate on foot or by bicycle.