Got back last week. Had a very nice time.
Cordoba has the Mezquita (the mosque the pp referred to) which is a lot more than she makes it sound.
Amazing actually - and it was also consecrated to a chruch when the Christians took over so the mix of cultures in one building is really interesting. Also there is the Real Alcazar - the old fortress/palace that has some very cool old ruins, arab baths, and a beautiful garden. There is also a medieval synagogue that is tiny but very cool when you think about the history and it's only .30 euros.
In Seville, please go see the Casa de Pilatos! It's sort of out of the way (though we walked to it and I'm pregnant, so it's not like a crazy far walk, just not in the main tourist area) and not a "major site" but was so very cool. It was built in the 1500s and has amazing mudejar tiles all over - they are like wall paper! And the gardens are so beautiful as well. The courtyard has a 5th century BC original statue of Athena. It's 5 euros to get in to the see the main floor and the gardens. So worth it. We spent an hour just staring at everything. You can pay a few Euros more for a tour of the upstairs - has some antiques and such, but it doesn't seem worth it. The real beauty is on the main level. Here are a couple pics:
There is also a bull ring in Seville that does bi-lingual tours every hour or so. We didn't go but it would have been interesting.
Madrid, if you don't want to see art at the Prado, the Royal Palace is very cool. The extravagance is crazy. Parque Retiro (kinds like their Central Park) is also very beautiful and worth a visit I think.