The Széchenyi Lánchíd — the Chain Bridge — is the reason Budapest is one city and not two. Before it opened in 1849, crossing the Danube meant a boat or a winter walk on the ice; the bridge stitched merchant Pest to royal Buda for good. Walk it the way it was meant to be walked, from the flat Pest bank up to the castle hill.
Come down from Vörösmarty tér to Széchenyi István tér, the Pest bridgehead named for the count who willed the bridge into being. Then cross. The stone lions have sat at the ends since 1852, and the middle of the span is the place to stop — the river below, the castle ahead, the Parliament downstream.
You land in Buda at Clark Ádám tér, named for the Scottish engineer who built the bridge and then drove the tunnel straight through the hill in front of you. The zero-kilometre stone marks where every Hungarian road begins. Finish on the Budavári Sikló, the 1870 funicular, riding the minute up to the castle and the view back over everything you've just crossed.