The archaeological site of Medina Azahara [various spellings] shows only a small fraction of the old city, built to demonstrate the power and prestige of Abd al-Rahman III, Caliph of Córdoba in the 10th century, when it was capital of Moorish Spain.

http://www.andalucia.com/magazine/english/ed4/madinat.htm will give you the history of its long period in the making, followed by a short existence.

There is enough to keep you entranced for a few hours. There is no ordinary service bus from Córdoba right to the site but there is now a tourist bus every morning that gives you the return trip, a reasonable time at the site and a guidebook in English [or other language.] You can book for this at the TIC or through most hotels.