If you are flying round-trip Madrid, and your flight arrives fairly early in the day, start in Cordoba. You can take the train from the airport to Madrid's Atocha station and then have a 2-hour train ride to Cordoba. Then finish your trip in Madrid, so you have easy access to the airport for your (potentially early) flight home. If you do that, then take the train or bus from Granada to Madrid. Otherwise Cordoba is as good a place to end as any, especially if you are flying home from Seville. If you have an afternoon or evening flight home from Madrid, it's doable.
It's much better to plan for nights than days. If you plan for 3 full days in Granada, for instance, you need 4 nights there. You "lose" almost 1/2 day with every move - packing, checking out, getting to train station, waiting for train, then the reverse and getting oriented to the new town.
Transportation - get a car when you leave Seville, drive through the pueblos blancos to Ronda, spend a day seeing the sights in Ronda, then drive to Granada and return the car. For the rest, the trains are better. The trains aren't currently getting all the way to Granada because of works on the tracks. Renfe has buses that take you from the train station in Granada to the train station nearest Granada, where you connect to the train to your destination. It's about as easy as taking the bus non-stop. If you're going to Cordoba, the bus and train stations are next door to each other. In Granada the bus station is not much farther from the center than the train station, only a few euros more by taxi. If you are going to Madrid, it may be easier to take the train and arrive at the main train station which is also a metro station.
Madrid - Hotel Europa. It's modern, comfortable, central, walking distance to the Prado and Thyssen, just meters from the metro and Cercanias (suburban train) stop, the HOHO bus stop.
Seville - Amadeus Hotel in the Juderia. Great hotel, great location.
