The Buda bank north of the Chain Bridge is built on hot springs — the reason this stretch has been a town of bathhouses since Roman times, and the quietest riverside walk in the city. It runs from the working baths down to the square that faces Parliament.
A little over three kilometres, best in the afternoon. Start at the Lukács, a bathhouse since the 1880s with a courtyard of thank-you plaques from cured patients, and the neighbouring Császár baths fed by their own warm lake — this is Felhévíz, 'hot water above', named for the springs. Walk south to the Király baths, a 1560s Ottoman dome with star-shaped glass set into the roof, built so a besieged garrison could still bathe.
Then down to the river under Rózsadomb, the villa-hill, where the embankment runs quiet below the traffic with Parliament strung along the far bank. Pass the elbow of Margaret Bridge, where the island points upstream.
Finish at Batthyány tér, square-on to the Parliament across the water, with the M2 and H5 below.