Slightly hidden within the Alhambra grounds is a building called Carmen de los Martires. Originally a 19th century home with a beautiful garden, this now government building is open to the public and sometimes used as an event venue. A long dirt path leads to the mansion that is lined with greenery and statues. Home to several peacocks, you can see these friendly birds hanging out near the home even during the winter.
The atmosphere is very peaceful when visiting this building and it is also free to visit. I would definitely recommend stopping by when visiting the Alhambra for a break from the crowds.