Madrid-Cordoba-Seville-Granada—what order to do these in?

My suggestion since you like wandering around old cities, with less traffic, is to mix in at least 4 days someplace small and less traveled. Extremadura has lots of options that fit the bill but Caceres might be a good option. Personally, 3-4 days is plenty for Sevilla and Granada so maybe steal some days there.

I’ve not been down to the White Hill Towns area but that’s a popular RS destination for soaking up that small town vibe. You could insert that in lieu of Extremadura, or better yet, do both since you have 4 days to play with.

The “counter clockwise” order makes sense. If you wanted to reverse it and do Extremadura at the end, that’s probably what I might do.

Any way you plan it, that list some backtracking, but only a few hours worth, total. I don't think there's a particularly better or worse way to route it.

I appreciate your languid pacing, but if you want to add a stop you could carve some time from Granada and Cordoba without feeling like you're short-changing those towns.

4 days is quite a bit for Cordoba. What about adding Ronda?

I'd do Madrid, Granada, Sevilla, Cordoba, Madrid to make a loop.

I'd also probably shave off 2 nights from Granada and maybe 1 night from Cordoba to put back into your piggybank of free nights for other locations.

Using those nights, I'd reinvest to spend some time in Cadiz, the foodie capital of Andalucia, and very popular to visit with local Spanish nowadays. Cadiz is the oldest city in western Europe.

As well I'd spend some time in the underrated province of Jaén, the capital of olive oil in Spain, just exploring those well preserved renaissance towns of the area, like Úbeda and Baeza.

By train, Cordoba's sort of on the way between each of the other city pairs, so it doesn't make a great deal of difference whether you do a clockwise or counterclockwise loop. There's less rail service in and out of Granada, so it's worth looking at the schedules to see whether there's a reason you might prefer to travel there from Seville rather than from Cordoba.

Others have suggested possible places where you could use the extra four days. I agree that you're allowing enough time for relaxed visits to Cordoba, Granada and Seville, but Seville's by far the largest, so that's the last place I'd want to cut time. I'll add these additional places to your "maybe" list:

Toledo
Segovia as a day trip from Madrid
Cuenca as a day trip from Madrid
Alcala de Henares as a day trip from Madrid
Salamanca as a day trip from Madrid
Ubeda/Baeza (best by bus from Madrid, and then on to Cordoba by bus)
Carmona as a day trip from Seville by bus
Priego de Cordoba as a day trip from Granada by bus

What we really enjoy is walking on old streets, walking in parks, visiting churches and old buildings, wandering around places with a lot of history

Given your interests, I’d definitely recommend adding Toledo to your itinerary.

My mom (88 at the time) and I spent 3 weeks in Spain, some years ago, and this was our itinerary:
Flew to Madrid > train to Córdoba on day of arrival (5N) > bus to Granada (4N) > bus to Sevilla (5N) > train to Toledo (5N) > Madrid (1N) > fly home.
The original plan had included Ronda (in between Granada and Sevilla) but opted to skip it in order to avoid 2 extra bus rides.
We’d already visited Madrid, on a previous trip, and we really wanted to experience being in Toledo instead of just spending a few hours there as a day trip (on previous trip)

You may consider saving visiting Madrid till the end of your trip, and thus avoiding an extra hotel change.

You may also want to consider visiting Ronda, Cádiz (day trip from Sevilla), Segovia (day trip from Madrid) and Zaragoza!

Wishing you a wonderful trip!

P.S. Do book your Alhambra Tickets as soon as your dates for Granada are set!

We traveled to Spain last year 9 Sep to 4 Oct. Very hot to roasting, but adapted by siesta in our apts with A/C. Barcelona (6 nites), flew to Granada (4), bus to Seville (4), train to Cordoba (4), and train to Madrid (7 with day trip to Toledo). We found plenty to do that was similar to your desires. If we could have done so, we would have added 1 or 2 nites in each place. Visited all the main places including museums, Moorish buildings, Modernista buildings, lots of gilded cathedrals, "happening" plazas & boulevards, and many old narrow streets. Your schedule looks good by our reckoning. Of particular note for evenings: Las Rambla (Barcelona); Plaza Neuva area (Granada); "Mushroom" shopping area (Seville); Roman Bridge (Cordoba); and Plaza Mayor area (Madrid). P.S., get A/C!

Six nights in Granada is a couple too many in my eyes, four is enough. I found Granada to be a rather workaday kind of city, much less romantic than your other stops. Even the medieval quarter felt small, and that I had walked every street a few times over. I think you would enjoy a couple nights in a place like Ronda a lot more, and it’s a logical stop between Granada and Seville.

Another poster mentioned Toledo, and I’d vote for that too. It tends to be more of a day trip destination, so by the evening it can feel like you have the town to yourself. Lots of twisting, medieval lanes to wander and great views surrounding the town. If you’re flying into Madrid, I’d recommend heading straight here. It’s an easy and frequent train, and a great place to get your feet wet.

You have a lot of days to play with, and while I appreciate the slow travel, I think you could add a couple destinations without taking away from your itinerary. Granada aside, all these cities are very well connected. There’s not much driving the order of your visit other than preference.