Thanks everyone for your suggestions!
Here is what we did—we had a fantastic time! I’ve also included what I would do differently next time.
Day 1
We drove from Seville to Rhonda stopping in Zahara to check out the town and climb up to the castle. This was meant to be a full hiking day— but it was pouring rain so we skipped the hiking and arrived to Rhonda early, did some sight seeing and attended a concert at the Guitar House, which was wonderful.
Day 2
We had a reservation to visit the Pieta Caves— which was well worth the time and then drove to Grazalema to visit the town in the late afternoon.
Day 3
On our way to Córdoba we drove to and hiked the Caminito del Rey.
We spent two nights in Cordoba, we liked taking our time here, but if you are on a tight schedule, a day trip would be enough to see the main sights.
What I would do differently.
Day 1
Drive from Seville to Acros de la Frontera for a quick visit. Continue to Grazelama ( side trip to Zaraha if you have time) Spend two nights here to dedicate a day to hiking in the area.
Note: the roads in the area are narrow by North American standards and it can be nerve racking when anticipating on coming traffic around blind corners. It can be a bit daunting if you are not a confident driver.
Day 2
Visit the Pieta cave
Spend afternoon Sight seeing in Rhonda, guitar house concert.
Day 3
visit and hike the Caminito del Rey on way to Granada. (Visit Cordoba as a day trip from Seville).