For me a trip isn’t complete without exploring the bridges. And since Budapest is literally two cities spanning the Danube River, it has some wonderful bridges. The Szabadság Bridge, which was built in the 19th century, is a blend of elegance and history. Ornate design, guardian lion statues, and city vistas make crossing it a visual treat. The road is completely separate from the pedestrian pavement, so it is surprisingly peaceful to run across.
The Erzsébet Bridge, built in the 1960’s is far more modern (and busy). The functional design still has some lovely lines though, and its quite astonishing how thick those cables are when you get up close.
A nice route to run is to cross the Erzsébet Bridge towards Buda (the castle), climb the stairs and run around the castle gardens, then head back to the river on the Northern side of the castle, and run back to Pest along the Szabadság Bridge.