Here’s some advice for future travelers: do Cordoba first, then Sevilla. It will be easier to appreciate Cordoba’s charms when not comparing to Sevilla’s.
Cordoba has an Alcázar. The palace is mostly ruined and nothing special. The gardens are wonderful, full of the noise of playing fountains and the intoxicating scent of jasmine.
Not far from the Alcázar sits the mass of a truly remarkable church. First a Visigoth (Christian) basilica, then a mosque, then a cathedral, the complex is the most eclectic amalgam of architectural styles I have seen. It’s stunning. Unlike the Alcázar in Seville, where the Christian king had the Muslim artisans build something new in the moorish style, the Cordovan building was built by each group as their own, outing their own distinct layers in top of the others in a form of appropriation and power. It’s layering, not blending. But still, it’s great fun to see the influence of Rome, Byzantium, the Muslims, the Christians, the gothic, renaissance, baroque and rococo all in one place. You could basically teach an art history course (and politico-religious history too) just walking through.