San Giovanni in Laterano is the cathedral of Rome, and almost nobody who isn't local knows it. St Peter's gets the crowds; this is the Pope's actual seat, the church that outranks it, sitting in an open quarter against the city wall on the far side of the centre. The walk is a tight loop around it and the strange relics gathered at its side.
Come up at Piazza di Porta San Giovanni and take the east front whole before going closer — statues along the roofline, the wall behind you. Inside the basilica, the colossal apostle statues and the Cosmatesque floor are worth the slow circuit; it's free and half-empty. Out on the north side stands the Lateran obelisk, the tallest in the world, fifteenth-century BC and carried from Karnak. Circle it.
Across the road, the Scala Santa — the stairs tradition says Christ climbed before Pilate, still climbed on knees today; take the side flight and look. Then the Porta Asinaria, the original fourth-century gate beside the modern arch. End down Via Emanuele Filiberto towards Manzoni, the everyday street that brings you back to earth.