The 17th-century, baroque Igreja de Nossa Senhora da Nazaré, decorated with attractive Dutch azulejos, is on the Promontório do Sítio and holds the much-venerated sculpture of the Virgin, said to have been made by Joseph himself in Nazareth when Jesus was a baby: hence the name of the town. For €1, you can get close to the statue itself – it's not too often that you get the chance to appear in the middle of an altarpiece.
Look out for paintings of a deer in mid-air that refer to the legend of the Virgin's appearance here. Though the fall was tragic for the animal itself, its look of surprise is amusing.