Take Calle Zamora down to Plaza Mayor (5 minutes) and then leave the square on Calle Prior, continuing on this street until Plaza de Monterrey. Here you'll find Monterrey Palace, the occasional residence of the Duke and Duchess of Alba, which is noteworthy for its two towers and three chimneys.
On the left is the church Iglesia de la Purísima, and a little further ahead, on the right, the convent Convento de las Úrsulas.
If you take Calle Domínguez Berrueta from here and turn right at Ramón y Cajal, you'll come to the Colegio del Arzobispo Fonseca (college of the Archbishop of Fonseca).