The Danube River defines Budapest geographically, if not historically and mentally. One one side you have proud UNESCO-recognized Buda, home of kings and aristocrats while on the other side you have Pest, Buda's down-at-heel sibling which is currently the heart of the city's thriving arts, nightlife, and cultural scenes.
When you first see the Danube, you'll understand why it's considered one of the most important rivers in the world. It’s massive, first of all, and connects many of the most important capitals of Europe in its slow crawl towards the delta. If you're planning on being in Budapest, I'd sincerely recommend taking a walk along the river banks right as the sun goes down. All of the city's major monuments like the Hungarian Parliament, the Fisherman's Bastion, Buda Castle, and its numerous bridges and palaces light up to create one of the most beautiful and romantic strolls imaginable.