Castle Hill is the postcard everyone arrives for, and the trick is to walk it so it stops being a postcard. The monuments are unavoidable; the empty lanes behind them are the reward.
About three kilometres, best early before the coach groups land. Skip the queue and climb the stepped path beside the Budavári Sikló — the funicular — saving the ride for the way down. Walk the spur first: Buda Castle, where the free terraces over the Danube beat most of the ticketed rooms inside.
Then north to Szentháromság tér for Mátyás-templom, its Zsolnay-tiled roof catching the light, and the Halászbástya (fishermen's bastion) behind it — the lower terrace is free and frames Parliament across the river perfectly. When the crowd thickens, escape into Úri utca and the cobbled lanes, where the Gothic doorway niches have stood for six hundred years and you'll have them alone.
Loop to the Bécsi kapu (Vienna Gate) at the quiet north end, back along the rampart, and ride the funicular down to Clark Ádám tér and the Chain Bridge.
