Toledo and Córdoba are a good choice.
Take an early train to Córdoba and taxi to Mesquita from the station.
Afterwards , you could visit another one or two places in the city that interest you the most.

Toledo is closer so you can see quite a few of the " attractions".

Hi there, don't write Cuenca to quickly. The fast train will have you there in no time and its different to the other daytrips suggested. That said on this next trip to Spain.. in 26 days but who's counting, our stops are Segovia (1st, landing in Madrid, directly on to train to Segovia, will be there in time for dinner!!), Madrid for Christmas, Malaga, Ronda, Cordoba, Madrid..
This time we are doing the drive to Consuegra to see the windmills, remember anywhere you decide it will be interesting and fun!!

Well, up until now I've strongly considered both Cuenca and Cordoba but truthfully the price tag for these train tickets high and getting higher. We may end up being less ambitious and go to Segovia and Toledo - so much less time-
and pocketbook-intensive. I could be convinced that Cordoba is worth it, though! I mean we've spent that much for a nice dinner out at home! So it can be justified, but that doesn't mean it wouldn't hurt to finalize the purchase! Bottom line, should we pay the $300 train ticket for a day trip to Cordoba?

Cordoba is delightful and the Mezquita is, IMO, among the world's gems. That said, you don't have time for everything. You might wait to visit Cordoba until you visit Sevilla and Grenada and can give them each the time they deserve.

Yes, AVE is expensive....

There are many options from Madrid. Choose what
suits you budget, time, interest and winter weather

Great advice from danon!

Thank you all for your suggestions. I love that there is a forum like this.