Matthias Church — formally the Church of Our Lady of Buda — is the coronation church of Hungarian kings, and it wears its history on its roof: a cascade of Zsolnay ceramic tiles in green, gold and rust, above a Gothic skeleton reinterpreted in the nineteenth century by the architect Frigyes Schulek. Step inside if the doors are open and you find diamond-patterned walls, painted vaults and a richness that is genuinely startling after the pale exterior. Schulek is also responsible for the fantasy next door. The Fisherman's Bastion, built around the turn of the twentieth century, is a neo-Romanesque confection of stairways, arcades and seven conical towers said to represent the seven Magyar chieftains who led the settlement of the basin.
It exists, essentially, to give the city a viewing terrace, and it succeeds: from the upper walkways you look straight across the Danube at the Parliament, the bridges and downtown Pest, which is the view every guidebook photographs. Late afternoon softens the light and thins the crowds, so this is the slot to linger, lean on the parapet and let the two of you have the panorama more or less to yourselves.