At the highest point is the Mirador ("lookout") of San Nicolás. An esplanade at the foot of a church from which there is a magnificent view of the Alhambra with the Sierra Nevada in the background. To reach the Mirador de San Nicolas the easiest way is to go up the wonderful little alleys of the Albayzin. You can go up Calle Caldererias, or Paseo de los Tristes or Cuesta Alhacaba and Plaza Larga.
If you don't feel like walking you can take the C1 or C2 minibuses that go through the Albayzin.