Rizos-
So sorry you will miss out on Madrid, but I envy the time you will have down south!
If you are spending any length of time in Seville, I would recommend renting an apartment from Sevilla5.com. We stayed in one of the apartments (Arfe) listed under 'personal style' and loved it!!
It is located in El Arenal, just a short walk from the Cathedral & Plaza Neuva.
Hope this helps!