Cordoba is best known for Mosque Cathedral of Cordoba, or "Mezquita" (Spanish for 'mosque'). It is one of Spain's major Historic Monuments and UNESCO World Heritage Site since 1984. Maybe it was the case of expecting too much because of its fame, but for me it ended as disappointment. Interior is undeniably spectacular, but never ending tourist hordes, even in low season, spoil overall feel. It is also quite dark inside, and although Photography is allowed, getting good shots is very difficult as setting the Tripod is out of question. But don't let this deter you; Mezquita is still spectacular and it should be on anyone list planning visit to this part of the World.
I enjoyed the most equally famous Roman Bridge across Guadalqivir River, dating from 1st centry BC. It reminded me strongly of Bridge over River Drina in Visegrad, Bosnia and I crossed it at least dozen times. On south side Torre de la Calahorra Fortress is well worth the visit, while on North side "Alcazar de los Reyes Cristianos" is a must. It is well worth spending full afternoon in this Moorish Palace with fantastic Garden; crowds thinned out towards closing time and allowed for some unexpectedly nice Photos.
Outside Town is Madīnat az-Zahrā, or Medina Azahara, a major Archeological site, and I enjoyed wondering around the ruins for few hours although some areas were closed. I also planned to visit Almodovar Del Rio Fortress, some 40km out of town, but didn't have enough time.
Timing is crucial for Cordoba; low season means fewer tourists but also chances of bad weather (it rained most every day during my visit). Andalucian summers are beautiful but also very hot; lady in Souvenir shop told me daytime temperatures are in high 30s or even low 40s. Springtime (March/April) is probably optimal. Travel logistics are straightforward because of Train Station that connects just about everywhere in Spain and is situated in walking distance to Old Town, where most travellers will want to stay.