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Germany’s capital city has undergone a renaissance in recent years. Emerging as one of Europe’s most culturally vibrant centers, Berlin is on the cutting edge when it comes to art, fashion, and nightlife, offering visitors a mix of glamour and grit. Hotel rates are around $100 per night. The city looks back at its dark history through powerful attractions such as the Checkpoint Charlie Museum and Topography of Terror. You can find flights from Boston and New York for about $300.