However, I cannot find any luggage storage facility for large bags near the train station in Cordoba.
It's in the bus station across the street. I used it last year but can't remember much about it.
We stayed in Madrid and Granada last October and have stayed in Malaga, Seville and Cordoba many times in the past. I think Cordoba's worth an overnight stop at least.
Spain is about nightlife to me (and I'm not young, it's for all ages) so my perspective might be different - but I don't think you see much of a Spanish city unless you overnight there. For a start, in Andalucia (and Madrid to an extent) most places are "closed for business" in the afternoon, then spring back into life about 8-9pm.