Andalusia from Madrid 8 or 9 nights by train

Consider a day trip to Segovia from Madrid, but I undersrand there is only so much time. In fact, I may suggest giving Madrid an extra day for that purpose.
I had similar interests and stayed near Atocha train station in Madrid. It helps that it is also near the museums and Retiro park.
For Andalucia, Seville and Granada should be your 2 locations as you can daytrip to Cordoba from Seville. For most, if the Alhambra is the prime ticket for Granada, 2 full days is sufficient (but I stayed 4). It is not a day trip from anywhere.
Seville, along the river and old town is lovely, with Marie Louisa Park. Wander over the bridge for dinner with the locals in Trianna.
As Cordoba is enroute to Madrid from eville, I would like to encourage you to do one more move and have at least an overnight rather than a day trip. There is more to see than the Alcazar and the Mezquita. To me, it is a town to meander it. Add the Jewish Quarter, and the often overlooked Archeological Museum...or head out to the old Roman archeological digs at Medina Azhara, and you may wish you had 2 nights.

I'd go south and work my way back. Maybe 4 nights in Sevilla, 2 in Cordoba, and then 2 in Granada. (If there's an extra night I'd add to Granada.)

You could a day trip to Cordoba, either out and back from Sevilla or as a stop-over on your way between Sevilla and Granada. (I believe there's luggage storage at/near the station.) Either way, it would have to be a planned, focused day.

We did a similar trip in 2017. We flew into Madrid and immediately traveled by train to Sevilla. After five nights there, we took the train to Cordoba for two nights. Then a bus to Granada for three nights. Finally, we finished with three nights in Madrid.

Certainly, you can tweak the nights in each place, but do put all your time in Madrid at the end.

Thanks everyone, I am definitely thinking of adding nights in Córdoba and heading south immediately and finishing in Madrid (a long travel day with flight but might save time later). This information is great.
Francis

Francis- Heading straight to Seville would be an efficient way to start. If you haven't booked flights yet, look at an 'open jaw' or 'multi-city', so you connect all the way to SVQ. And if you do have flights booked, maybe call the airline to see how much it might cost to change. I'd consider it worth some money to simplify the trip.

Have you made your airline reservations yet? If not, can you do open-jaw (multi-city)? Into Madrid and home from Seville. This means you don't have to waste time backtracking to Madrid.

This is how I would allocate the nights:
Madrid - 5 nights with a daytrip to Toledo OR
Madrid - 4 nights and
Toledo - 1 night
Cordoba - 2 nights
Granada - 2 nights
Seville - 4 nights

Thanks all. I've already bought round trip tickets though I might check on price to change (I looked at some open jaw options and they were relatively expensive). This is great information.
Francis