A coastal town just 20 miles west of Lisbon, Cascais was once a small fishing village, but its idyllic scenery attracted the attention of artists, writers and expelled European nobility in the 20th century. Today, it still attracts high society, but all society comes in force to enjoy the gorgeous beaches and adventure options like sailing and surfing. The Conde de Castro Guimarães Museum, a former palace, is now open to the public and displays an impressive collection of art and artifacts.

Time seems to stand still in Evora, a well-preserved medieval town that features protective walls, a 13th-century cathedral, several palaces,and a 1st-century Roman temple. No surprise that the town center is a UNESCO World Heritage Site. Even though it’s kind of creepy, don’t miss the Chapel of Bones, where the remains of nuns and monks are arranged in a haunting mosaic.

Though probably best known as the capital of West Germany from 1949 to 1990 (and of reunified Germany until 1999), Bonn actually has a history dating back to the 1st century BC. Roman soldiers were stationed here and the largest known Roman fort was built at Bonn. In medieval times, the town gained prominence when the Archbishop of Cologne transferred his seat to Bonn. The city's most famous son is Ludwig van Beethoven, born in 1770 at Bonngasse, where a museum now honors him.

It’s nicknamed the Eternal City for a reason. In Rome, you can drink from a street fountain fed by an ancient aqueduct. Or see the same profile on a statue in the Capitoline Museum and the guy making your cappuccino. (Which, of course, you know never to order after 11 am.) Rome is also a city of contrasts—what other place on earth could be home to both the Vatican and La Dolce Vita?

The first time you go to New York, go ahead and be a sight-seer—everyone should visit the Statue of Liberty, the Met, Times Square, etc. But on a return trip, pick a neighbourhood and go deep. You’ll find hole-in-the-wall bars, great delis, quirky shops… exploring the non-touristy side of New York is an incredibly rewarding experience for a traveller.