Rózsadomb — Rose Hill — is where Budapest keeps its money and, improbably, its holiest Muslim shrine. The two sit together on the same green slope above the river, and walking up to one and on through the other is one of the city's quietest pleasures.
Around three and a half kilometres, a steep start then easy, best in the afternoon. From the Margit híd bridgehead, climb the cobbled Gül Baba utca, worn by four hundred years of pilgrims, to the octagonal türbe (tomb) of Gül Baba — a dervish who died here in 1541, and the northernmost Muslim pilgrimage site in Europe. Cover up, take off your shoes, and go in; it's sacred, not a sight.
The rose terrace around it gives the hill its name — gül is rose — and a wide view back over Pest. Climb on into the villa streets, Mecset utca and the lanes above, where art-nouveau houses hide behind gardens.
Wind down to the Bem rakpart with Parliament reappearing across the water, and back to the trams at the bridge.