The Iglesia de la Vera Cruz sits just outside the city walls, a squat twelve-sided Romanesque church built by the Knights Templar in 1208. It is the finest Templar church in Castile and one of the most unusual medieval buildings in Spain — its unusual plan copies the Church of the Holy Sepulchre in Jerusalem, with a small inner rotunda where the Order held its secret ceremonies. The church was abandoned for centuries after the Templars were dissolved and is now maintained by the Order of Malta.
The walk from the old city takes about fifteen minutes and passes through a pretty park — the views back across to the Alcázar on the cliff are exceptional from this side. The church is open most days with modest entry fee, and the visit is quick: the interior is small and austere, which is the point. Come in the morning when the light hits the old stone.