Given that I have discussed symmetry in Islamic art for a couple of decades in my Space class, I wanted to make sure we would visit the Alhambra, and we did, towards the end of our trip.
The Alhambra is an architectural marvel, and Spain's most visited site. (More info on Wikipedia.) For a math teacher, it is remarkable in the variety of the symmetric patterns in the tile designs and stonework. Apparently, a young M.C. Escher visited the Alhambra and was inspired to explore tilings and symmetry in his artwork.
Oh, and speaking of symmetry in art, the Reina Sofia museum in Madrid had an exhibit of Latin American geometric abstract art from the middle of the 20th century. Two examples:
Like these two, many works in that exhibit had two-fold rotational symmetry. See more examples on the exhibit's own Web site: Concrete Invention.
Knowing that we would end up at the Alhambra, I took pictures of symmetric designs whenever I thought of it during the trip. You can see more here, culminating with my Alhambra photos. (Click on the first photo to see the photos one at a time -- a few have captions.)