The dazzling Danube River cuts right through the middle of Budapest, creating two distinct and equally essential parts of the city; Buda and Pest. The Buda side is calm–offering a majestic castle reminiscent of the Ottoman Empire, rolling green hills, and a classic, cobblestoned Old Town. Meanwhile, the Pest side is lively–packed with tree-lined avenues, architecture that crumbles with charm, and an…