The greatest cities of the world got their reputations for a reason. But for every Paris—with its fine dining and twinkling Eiffel Tower—there’s a Bordeaux, where you can nibble Michelin-starred seared duck liver while overlooking the eighteenth-century Palais de la Bourse (without the fear of running into your across-the-hall neighbor). For every London, a shopper’s and book lover’s paradise, there’s a Birmingham, which has both a 250-year-old jewelry quarter and a new, $300 million library�plus hotels that won’t cost you a small fortune. There may be sprawling galleries and clubs in Berlin, but there’s also an emerging art and nightlife scene (minus the mass gentrification) in Leipzig. So for this, our annual winter-travel guide, we’ve turned the lens on ten such long-overshadowed cities, along with some under-the-radar beaches and ski towns. They may not sell as many guidebooks as their A-list counterparts, but they have just as much charm and excitement�with way, way fewer tourists.