I am planning to spend 8 nights in Spain with my wife and son during the last 2 weeks of November. We are flying into Madrid and out of Barcelona. I have this tentative itinerary in mind. 3 nights in Madrid, 2 nights in Cordoba, 3 nights in Barcelona. I'm also open to cutting 1 night out of Cordoba and spending an extra night in Madrid or Barcelona. I've also gone back and forth between Cordoba, Sevilla, and Valencia as the third city but Sevilla seems a bit too far. (I've been to Sevilla before and loved it, but this will be my family's first trip to Spain). Interest are experiencing the Spanish culture, walking around, food, architecture, history.
One possible option. How does this sound?
Day 1: Arrive in Madrid at 8:30 AM from USA
Day 2: Madrid
Day 3: Day trip to Toledo or Segovia
Day 4: Train to Cordoba
Day 5: All day Cordoba
Day 6: Train to Barcelona AM
Day 7: Barcelona
Day 8: All day Barcelona or Montserrat
Day 9: Fly back home