The Alhambra
This place was the last muslin resort in Spain. There are several places here:

The Nasrid palaces are the most known, in fact, the name "Alhambra" comes from the red color of its walls. This collection of beautiful gardens, fountains, channels and richly decorated rooms was built by Ibn Ahmar in the 13th century, and by his successors. Here lived the Catholic Kings after they conquered the last muslin redoubt in Spain. Among the most beautiful places you will find are:

• The Mexuar or reception hall.
• The Court of Partal.
• The Court of the Arrayanes, where is the hall of Ambassadors.
• The Royal Baths decorated in rich mosaics.
• The Harem includes the wordly known Court of Lions and the Hall of Abencerrajes, that posses the most beautiful stalactites ceiling and the fountain where executions where accomplished.

The Generalife is a splendid garden delicately built, with sculpted trees and water flowing by staircases.

The Alcazaba is the old military fortress. Near is the Renaissance Palace built by Catholic Kings' grandson, ina totally different style, where you may visit the Alhambra Museum..

The Royal Chapel & Cathedral
Close to the Cathedral is the Royal Chapel, which was built like gothic style mausoleum for Catholic kings, her daughter and her husband. Sculpture of the kings is a very realistic one. You may watch the crown of the Queen and the sword of the king.

Other places
At the Sacromonte Mount, you will get fantastic views of the city, the mountains and the Alhambra itself, while walking by its quiet white streets, with windows crowded with plant pots, caves in the mount that are still dwelled and flamenco artists.

To the south of the city, The Sierra Nevada offers ski possibilities during much of the year. Beautiful landscapes, unique flora and fauna and the tallest peak of Spain can be seen here.

More info at:
      . http://www.alhambra.org