I second the recommendations for Baeza and Úbeda not too far from Granada. They are both World Heritage sites. I first heard about them here on this forum and after seeing photos of them on internet and Instagram, I decided that I had to visit them someday. I just got back from a long trip to Europe and when in Spain spent three nights in Baeza. Both towns are beautiful, with lots of alleyways and wonderful buildings to explore. The historic old town areas are not too big and easily walkable. We chose to stay in Baeza, the smaller of the two and enjoyed it very much but either would be great for a stay. They are only a few miles apart. We took a short bus ride over to explore Úbeda for the day and it was also fascinating. Both towns are surrounded by olive groves as far as the eye can see. Baeza has a "mirador" - look out point- with wonderful panoramic views of the Guadalquivir valley. We also visited an olive oil plant in Begíjar, right outside of Baeza, and it was very interesting to learn about olive oil production and taste different types of olive oil. From Baeza we took a bus to Jaén and stayed there just one night, but that gave us enough time to walk to the major sites in town and the next morning we took a cab up the mountainside to the castle and parador ( no public transport up there) for more great views.
From Toledo, Consuegra and its windmills and castle is a great visit and on the way there you pass through or close to the tiny town of Orgaz. In Toledo, the famous Goya painting of the Burial of the Count of Orgaz is on display at the Santo Tomé church. A few years ago, on the way to Consuegra, we decided to stop in the town and walk around. They were having some kind of festival there at the plaza and it turned into a very pleasant stop.
I did not get to Córdoba on this trip but if you do go there, look into exploring the nearby town of Écija.
