The Basilica of Nuestra Senora del Prado stands in a green park east of the old centre and is famous for its ceramic decoration. If the museum gives you the history of Talavera pottery, the basilica shows it at devotional scale: tiles, panels and colour worked into a living church.
The building is a favourite local sanctuary, so visit respectfully and give yourself time to look at the tilework rather than only the altar. The surrounding gardens make it a pleasant pause, especially in hot weather when the old centre can feel hard and bright.