We will be in Seville in December and wanting to stop in Cordoba and some other towns on the way to Granda where we will be staying a few days. I am looking for a private driver to pick us up in Seville and take us to some of the towns along the way, ending in Granada that night. Any suggestions on where to look? There will be 4 of us.
I think that Cordoba merits more than a quick stop between two points.
Have a think about using the train and staying at least one night in Cordoba - two is better to give you one full day.
The other towns en route are very small and mostly look the same - white towns.
Cordoba is worth 2 or more nights and can certainly fill all your time as you relocate from Seville to Granada. For that, taking trains would be best.
If traveling by car, Cordoba isn't on the fastest route from Seville to Granada. (A look at a map will confirm this.) The white villages most often targeted by US tourists who want to see something outside the major cities are located well south of that direct car route, thus adding considerably to the driving time.
Because of the geography, I think you need to choose between Cordoba and one or more white villages to the south.
I've only taken trains and buses in Spain, but quite a few people on the forum have used DayTrip (not necessarily in Spain) for inter-city travel with sightseeing stops along the way. I'd check that company out. I bet they offer a transfer that includes stops in one or more of Arcos de la Frontera, Grazalema and Zahara de la Sierra.
Daytrip might work for you.
Daytrip: Private Car Transfers with Sightseeing https://share.google/G0u9F3zNzG7yn6XKU
This is a very respected company they will drive you contact for price information.
We used Daytrip.con last April for this exact reason. We used them from Granada to Ronda (stayed 2nights in Ronda) then Ronda to Sevilla. If you pop in your origin and destination, it will suggest stops along the way. You can add as many towns as you want and adjust the length of time you want to stay at each stop. It was great to just be dropped off and have someone keep an eye on your belongings. We stopped at Setenil de las Bodegas, and Antequerra on each respective trip. Split between 4 people, I think the cost is very reasonable and worth it!
I have been to Cordoba before and I agree it’s worth at least one night to see the Mezquita and the beautiful patios with flowers.
I've used DayTrip and they are great. I've used them for several locations: daytrip.com