Whether it is one of Europe’s great travel destinations probably depends how you define that term. Though it may lack Rome’s antiquities, London’s sophistication, and the romance of Paris, no other European city can match its risk-taking, cutting-edge style, its extraordinary contemporary architecture, or its ability to get the visitor in touch with some of the 20th century’s most significant events.

Of course, we are talking about Berlin, a town that has undergone the municipal equivalent of a face-lift, tummy-tuck, liposuction and multiple organ transplants. It seems only yesterday that it was two cities, one dispirited and crumbling, the other vital and lively but hemmed in by concrete, barbed wire, and armed watchtowers. Traces of the divided city can still be found, but they are fast disappearing.

Berlin is a city of cultural as well as urban renewal, with frequent openings of new and restored museums, monuments, and institutions. A prime example opened in 2006: the spectacular, glass-canopied, multilevelLehrter Bahnhof, said to be Europe’s largest transportation hub, able to handle nearly a quarter of a million passengers daily. Another fairly recent addition to the long list of Berlin must-see destinations is the haunting Memorial to the Murdered Jews of Europe, a short distance from the Brandenburg Gate.

Berlin is also a place of vast parks and waterways, nonstop nightlife, Germany’s best shopping, and the finest and most varied cuisine of any city in the Germanic world. Best of all, its hotels and restaurants are priced lower than any major city in western Europe.

"The most important duty of the Mayor of Munich" said the grade school teacher of a former Munich Oberbürgermeister, "is to properly tap the first keg at Oktoberfest."

Eight million people may descend on this alpine city by the Isar every year for the world's largest beer festival, but for the rest of the year many travelers severely underuse this fascinating capital. Sure, everyone's been to Munich, but few stick around long enough to truly uncover the jewels of this modern medieval city. That's a mistake.

When most of the world imagines Munich and things German, it conjures up pictures of rotund, moustachioed, lederhosen-clad men and bodice-busting, dirndl-skirted women. And they're all standing around downing buckets of beer and gazing Alpwards. Well, that's how some of the citizenry looks – at least some of the time!

Though Munich is an anachronism, it is also cutting edge. Look round and you'll see one of Germany's most progressive, modern cities, an island of Europe's new high-tech industrial prowess and corporate headquarters of multinational power players like BMW, Siemens, and Bayer Pharmaceutical.

Munich's charm is in these contrasts, between the old and the new. It is a city in which starched businesspeople can be glimpsed in the nude on weekends – sunbathing in the magnificent English Garden.

It is a conservative stronghold where strict adherence to traditional German values somehow finds room to not just tolerate but cultivate a lively arts scene and some of the country's most controversial nightlife.

All this makes Munich one of the best bases from which to explore today's German experience. In the city, treat yourself to the newly renovated Alte Pinakothek, with its world class collection of classical European art that can once again be enjoyed; visit the castle of Nymphenburg and the family residence of the Wittelsbachs.

And within an hour and a half you can be in the Tyrolean Alps, or on the shores of lakes Constance, Chiemsee and Starnberg, or witnessing the majesty of Castle Neuschwanstein in Füssen.

Explore from your Munich base the eye-popping splendor of the northern Alpine villages of Garmisch-Partenkirchen - where you can ride a cable car to the top of the Zugspitze - Germany's highest mountain - the musical city of Mittenwald and the kitschy yet compelling buildings of Oberammergau.

Or head east to the glorious mountains and valleys around Berchtesgaden. And with a bit more time, take an overnight break in Prague, Vienna or Salzburg.

For seeing Munich, a good strategy is to get an early start and spend your first day discovering – or rediscovering – its treasure trove of museums, and grazing for culinary treats throughout the day.