We will be Sevilla for five days on business and wish to visit Cordoba before renting a car and driving to Cadiz, Tarifa, the White Villages, Granada and Madrid. Would it be best to rent the car two days earlier and drive to Cordoba, spend two nights and then backtrack to Cadiz, or take the train to Cordoba, spend one day, and return that afternoon by train. Then the next morning, we could rent a car and continue our trip.
For me the best option would be take the AVE train to Cordoba and spend two nights there. The real charm of Cordoba comes out in the golden hours of the afternoon, when all the daytripers from Sevilla have left and one can explore Cordoba's whitewashed streets in relative peace. This is only possible by spending the night there.
However, renting out a car just to drive all the way to Cordoba and then backtrack all the way south down to Cadiz does not make sense, both logistically and economically. Take the AVE back to Sevilla and then rent the car from there, you'll probably have a much better selection than in Cordoba anyways.
Agree with Carlos, and there are at least 3 car rental locations at the Sevilla train station. (Santa Justa)
Rent the car in Sevilla, go to Cadiz, Tarifa (why??), pueblos blancos (via Arcos, El Bosque, Grazalema, Ronda, Sentinel, Antequera), Granada. Then take the bus or train to Cordoba for at least one night, train to Madrid.