Víziváros — Watertown — is the thin strip of old Buda squeezed between the river and the castle cliff, named for the fishermen and tanners who once needed the water. It's where you come for the view the postcards steal: Parliament, entire, across the Danube.
Under three kilometres, best in the late afternoon when the light swings round onto Pest. Start at Batthyány tér, straight out of the M2, and look across the water — there's no better free angle on Parliament in the city. Behind you, Szent Anna-templom hides a baroque interior worth ten quiet minutes, and the old market hall sells the everyday.
Walk south along the embankment to the Kapucinus templom, where Ottoman window arches still show in the brick from its years as a mosque — the kind of layered detail Buda does so well. Then turn off Fő utca into the steep stepped lanes climbing toward the castle wall, residential and almost silent.
Land at Clark Ádám tér, the zero-kilometre stone, and the Lánchíd. Cross into Pest, or take tram 19 along the river.