Following Calle de los Reyes Católicos on the right, you'll come to the monastery Monasterio de San Juan de los Reyes. An example of Spanish Elizabethan Gothic architecture, it is the most important building erected by the Catholic Monarchs. The monastery is a memorial to the achievements of the Catholic Monarchs and their political policies. While the cloister is pretty (2.50€), viewing it from the outside is sufficient.
Head up Calle Pintor Matías Moreno and turn right onto Calandrajas Hill. You'll eventually come to Paseo de la Virgen de Gracia, which offers great views of the monastery.
Go up Travesía de Virgen de Gracia until the school for girls Colegio de Doncellas Nobles and then turn right onto Calle San Clemente. At the end of the street, you'll see the Portada de San Clemente (San Clemente's Front).
Turn right onto Calle San Román, which will take you to Plaza del Padre Juan de Mariana. Here you'll find the San Ildefonso church and the coffee bar La Flor de la Esquina, which has very nice outdoor seating with views of the Cathedral tower. It's ideal for a coffee (1€) or soft drink (2€) or a little snack (pork loin sandwiches with peppers and ham or Iberian ham with tomato 2€).
Continue up Calle Alfonso X el Sabio and turn right into Plaza Amador de los Ríos. Follow picturesque Calle San Ginés. Turn right onto Calle de la Plata and then left at Calle de Comercio, which leads into Plaza Zocodover square.