One of the most heart-pumping stretches of the Tour de France is always the 21 hairpin curves at L'Alpe d'Huez. Doesn’t sound so hard? They bike up the mountain. Every summer, hundreds of amateur cyclists flock to this resort in the French Alps and make the same climb. It’s more famous as a warm-weather destination, but L'Alpe d'Huez is also one of Europe’s top ski destinations. The nearby slopes appeal to beginners, but they get more challenging a bit farther away. More experienced skiers and snowboarders can literally travel for miles on some of the most challenging runs. And there are plenty of off-piste areas, too.

This beautiful fishing town on the Mediterranean Sea glimmers with sunshine and charm—so much so that Vincent van Gogh captured the streets and seascape of Saintes-Marie-de-la-Mer. In between lunching and shopping, visit the monolithic Church of Three Saints, a stone Romanesque church that was built in the 12th century. That, plus museums and bullfight arenas, will stimulate your cultural yens. Savour fresh fish and plump shellfish at any one of Sainte-Marie-de-la-Mer’s exquisite cafes and restaurants.

With half a million people, Nuremberg is Bavaria's second largest city. While its history dates to the 11th century, Nuremberg is most often linked to the 20th century (specifically World War II). It first served as the site of many pre-war Nazi rallies, then was nearly levelled by Allied bombing, then was the site of the famous post-war Nuremberg Trials. The city has much to offer today's visitors, including the rebuilt Nuremberg Castle and the world-famous gingerbread at Hauptmarkt. Hansel and Gretel would have loved this place.

Amsterdam is truly a biker’s city, although pedaling along the labyrinthine streets can get a little chaotic. Stick to walking and you won’t be disappointed. The gentle canals make a perfect backdrop for exploring the Jordaan and Rembrandtplein square. Pop into the Red Light District if you must—if only so you can say you’ve been there. The Anne Frank House is one of the most moving experiences a traveller can have, and the Van Gogh Museum boasts a sensational collection of works.

The kings of the Wodeyar dynasty set the bar high for the southern cultural capital of Mysore. Ornate palaces and the Gothic St. Philomena's Church with its 175-foot spires pack a visual punch; local institutions keep Carnatic classical music and dance in the public eye. A prominent 11th-century temple sits atop 1,000 steps on the city's outskirts. Dress to the nines and party like a rock star in celebration of Mysore heritage during the lively Dussehra festival, held for 10 days in October/November.