If you walk up Calle de Juan de la Fuente towards Calle de San Pablo, you'll come to the square Plaza de Colón. Behind it, on the right, is the Torre del Clavero (Clavero Tower), even prettier when lit up at night.
Going up Calle de San Pablo until it ends, you'll find Palacio de la Salina (Salina Palace) on the left, a Renaissance building from the 16th century that was originally used as a salt warehouse (today it is the headquarters of the Provincial Council). Four arches decorated with different busts, among which those of Cleopatra and Marc Anthony stand out, form its facade. It's worth entering to take a peek at the interior patio, a mix of Gothic and Renaissance styles.