We'll be flying in and out of Madrid, which we have visited before. Here's what I'm thinking (this would be early Oct):
-- arrive Madrid airport, train to Atocha and then on to Cordoba- 3 nights. Maybe a little long, but also time to recover. And we're "slow travelers".
-- train or bus to Granada, 3 nights.
-- train or bus to Seville, 5 nights.
-- train back to Madrid, 2 nights. Stay near Atocha for day trip to Toledo next day. Then the next day we fly out.