Edinburgh is unique among Scotland's cities. Tourism, its proximity to England, and its multicultural population set it apart. There's up-to-the-nanosecond dance clubs in 15th-century buildings and fire-breathers outside Georgian mansions: this is a place that knows how to blend ancient and modern. Edinburgh's superb architecture ranges from ancient churches to monumental Victorian masterpieces - all dominated by a castle on a precipitous crag in the city's heart. Pick any street to stroll - you'll be wowed by sudden vistas of looming battlements, cold volcanic peaks and hills steeped in memory.

Amsterdam is one of the world's best hangouts, a canny blend of old and new: radical squatter art installations hang off 17th-century eaves; BMWs give way to bicycles; and triple-strength monk-made beer is drunk in gleaming, minimalist cafes. The city seems to thrive on its mix and, despite hordes of tourists, still manages to feel quintessentially Dutch. The old crooked houses, the cobbled streets, the tree-lined canals and the generous parks all contribute to the atmosphere.

The now and the next are invented daily in Milan, Europe's creative capital. Until Milan led the way, who knew that happy hour could last four hours, that clothing and household appliances could be made out of basketry, and that coffee could make a delicious pasta sauce? This city is all about worldly pleasures. Shopping is of quasi-religious significance. Theatre and cinema flourish in this fashionable milieu, as does a hopping club scene and a slew of tempting restaurants. Apart from a few gems, the city is not renowned for its looks; it's lifestyle that counts.

Proper citizens of Vienna, it has been said, waltz only from the waist down, holding their upper bodies ramrod straight while whirling around the crowded dance floor. The movement resulting from this correct posture is breathtaking in its sweep and splendour, and its elegant coupling of free-wheeling exuberance and rigid formality -- of license and constraint -- is quintessentially Viennese. The town palaces all over the inner city -- built mostly during the 18th century -- present in stone and stucco a similar artful synthesis. They make Vienna a Baroque city that is, at its best, an architectural waltz.

The city is a haven for all sorts of culture, with a staggering array of museums, a vibrant arts scene and the infamous revels of Oktoberfest. Bavaria is souvenir-icon Germany at its postcard best, and the fairy-tale Gothic, Biergarten -filled city of Munich is no exception.

Frankfurt is often seen only as a transit hub or a business centre, but it's so much more. It boasts Germany's most spectacular skyline, mirrored in the Main River, and Europe's tallest office building. It's also the country's most international town; more than a quarter of its citizens are foreign. Frankfurt throws more money at the arts than any other European city, so you'll most likely catch a ground-breaking exhibition at one of its museums. And if you do happen to get stuck at the mega-airport there's a nightclub, art gallery and X-rated cinema to help while away those in-transit hours.