This is probably stating the very very obvious, but don't miss the Mezquita in Cordoba and the Alhambra in Granada - two of my favourite buildings anywhere in Europe. For the Alhambra, if at all possible try to book tickets in advance, otherwise you could face a VERY long queue. You can book online at
http://www.alhambratickets.com/.
In Cordoba, the area around Plaza de la Corredera is very nice to wander - much quieter than the streets around the Mezquita, which are lovely but sometimes crammed with tourists. Also if you have time, you might enjoy a visit to Medina Azahara, a ruined palace a short way out of town - if you don't have a car the tourist office runs daily visits.
In Seville just about everyone climbs the Giralda (Cathedral tower) for great views of the whole city. The Alcazar and gardens are also lovely, and I really enjoyed the Casa de Pilatos. If you want a break from the city, the smaller town of Carmona is nearby and has great views over the plain of the Guadalquivir river.
I personally didn't find the centre of Madrid as interesting as other Spanish cities, but Madrid is a good base for daytrips to Toledo, Segovia, and El Escorial.
Not sure what method of transport you will be using, if going by train don't leave it too late to book tickets (especially the high-speed AVE) as queues at the stations can be very long - at weekends tickets can even sell out.