Granada The Alhambra Palace and gardens
Cordoba Study the Moorish architecture of the Mezquita and La Medina Azahara, explore the myriad of streets in the old Jewish quarter, visit the gardens
Ronda a beautiful white town just over an hour from El Molino del Conde on the edge of Grazalema Natural Park. Ronda's best known feature is the 'El Tajo' gorge that divides the old and new town. The gorge is spanned by an amazing arched bridge over the 330 foot gorge and also by an old Roman bridge.
Malaga the Picasso Museum and the Carmen von Thyssen art gallery.
You might also want to visit Antequera, Priego de Cordoba or Zuheros.
For more information and ideas for day trips, see Trips, Visits and Activities.