Need help! A week in Andalucia - semi-traditional approach :)

Since Granada is higher up elevation wise go there first because Granada gets cold during the winter months and make this your first base. The second base should be Cordoba and the third Ronda which is a good jumping off point to visit Jerez and Arcos.

On Jerez vs. Arcos: I visited Jerez de la Frontera in December, 2019, and thought it was great. I haven't been to Arcos, so I can't do a comparison, but if it's a question of sherry, you can't go wrong in Jerez. There were small tabancos (sherry bars) everywhere, most sort of half-quaint, half-plain. Likewise flamenco -- Jerez seemed truly to be a real flamenco town. I don't know whether my early December visit was characteristic or not, but I encountered flamenco everywhere. There were live performances in several of the tabancos I mentioned -- no reservation necessary; travelling solo I just slipped in whenever I heard flamenco coming from inside. The flamenco ensembles were small, just trios, and the tabancos were packed -- at least in my opinion, though Spain doesn't seem to recognize the concept. (As I said, I always managed to slip in, and just as I thought you couldn't fit in another person, a small group would enter with ease). Anyway, it was a great experience. There were also larger venues offering flamenco. And around town, I also heard flamenco coming from speakers on lampposts, or piped into cafes; and on at least three occasions, people at near-by sidewalk cafe tables broke out briefly into flamenco song or dance.

I don't want to draw too many generalizations from one four-day stay in December, but I came away from Jerez with a great first impression. A couple of other things about sherry in Jerez: first, you can of course do tours of sherry bodegas; and second, in a real Jerez tabanco, you don't order "sherry"; you state your preferred kind: amontillado, manzanilla, oloroso, etc.

All the main sherry bodegas (Tío Pepe, Osborne, Williams & Humbert, etc.) are in and around Jerez de la Frontera. You can walk to many tastings and tours in town. Arcos is only a 30 minutes drive from Jerez.

Popular white towns most tourists seem to visit include Arcos, Grazalema, and Zahara de la Sierra. Of course there is Ronda just past those. There are a number of other towns, none of which take long to see. Just my opinion, unless you’re going hiking most are best seen from a distance where you can see the white painted buildings silhouetted by the surrounding hills. From Jerez you could take a day trip and do a circular route passing many of the towns. The route being, the area between Arcos and Ronda.

In November pools, other than possible along the touristy Costa Del Sol, will most likely be closed. The tourist season ends around mid-September and many small tourist towns along the coast essentially close up for the winter. Check the Paradors in Arcos and Ronda as they may have pools.

When we drove from Cordoba to Granada, we drove past some white towns. We did admire them from the road. Our stopping point, roughly halfway, was Antequara, which was chosen because it was halfway. In fact, if the hotel in Granada could have taken us a day early (I called from the road) we would have not stopped.
FYI: Smithsonian Travels is offering a one week stay in Antequera.

Antequara remains a high point of our trip. A small town of just over 45,000 people, and everyone was so friendly. There are Dolmans (which have been designated as World Heritage Site by UNESCO ) and hiking and Lobo Park with guided wolf tours. Antequera is architecturally beautiful, and has 33 churches, a magnificent Alcazaba (Moor fortress), museums, art exhibitions, and over 100 restaurants and bars.
We stayed in Hotel Mesón El Número Uno which is brilliantly located. (A 2 star hotel and really inexpensive, which was part of the reason I would have driven on to Granada if the hotel there could have taken us) There was secure parking across the street, the place was immaculately clean, although not at all fancy, but very comfortable. They have free wifi and a restaurant. We had reservations at a fancy resto. When we walked in and saw the kitchen and the two older women cooking and the smells of deliciousness, we asked to eat there and cancelled our other reservation. Just an awesome decision. They all treated us like family. Warm, outgoing, happy to have a hotel and welcome people to their home. Just amazing.
The TI is located at Calle Encarnación, 4, 29200 near one of the city's most symbolic squares, San Sebastián. There are English speakers there, they offer great advice. Their hours are Monday to Saturday and bank holidays, 9.30 am to 7 pm. Sundays, from 10 am to 2 pm.