Is there a preferred ordered for Cordoba, Granada, & Sevilla - flying in and out of Madrid

Not really. I chose Cordoba to start the closest place.
Are you spending time in Madrid before/after?

High-Seed train times and sequence: Madrid-3.5 hrs-Granada- 1.5 hrs Cordoba- :45- Seville- 2:40- Madrid
This sequence requires no backtracking, as reversing it would.
www.TheTrainline.com

When you travel by train, Cordoba is on the way from Madrid to Seville and from Granada to Madrid. In many/most cases it's on the way from Seville to Granada as well. That isn't obvious from looking at a road map, but it's the way the express rail lines run. Therefore, Cordoba can realistically fall anywhere on this itinerary. There's not a great deal of fast rail service into and out of Granada, so the schedule might be more attractive for one routing than another.

No matter what the order is, I now see you pass through Cordoba two times.

Note that there are only 3 trains each day traveling between Madrid and Granada. One morning train— probably the one to reserve— one afternoon train, one evening train,
Don’t wait to buy your tix since the trains easily could sell out .
Between Seville and Granada, only Renfe does this route in less than three hours and tickets are about $55.
The Alsa bus company runs this route in about 3 hours for $27 . And there are a lot more buses scheduled than trains.

www.Busbud.com
www.TheTrainline.com
www.Iryo.eu
www.Renfe.com

When my mom and I visited Andalucía, we flew to Madrid and took the train to Córdoba on day of arrival. We then took the ALSA Bus to Granada, then the ALSA bus to Sevilla, then the high speed AVE train back to Madrid and ended our trip in Toledo.
We spent the night before our flight home near the airport but we’d visited Madrid on a previous trip.

The main reason for choosing this route was because it worked great logistically. We also chose to travel by bus to/from Granada due to more time options.

Once you decide on the route you want to take, make sure you book your Alhambra tickets soon.

Enjoy your time in beautiful Spain!

For our trip we flew into Madrid and home from Seville. We used ALSA buses and the trains. This was our order, if it helps. (We visited two places not on your list.) I would say the order depends on bus and train schedules.

Madrid
Toledo
Cordoba
Granada
Malaga
Seville

Based on the AVE train I'd go

Madrid
Toledo/Cordoba
Granada
Sevilla
Madrid.

I always arrange my trip so that I'm in Granada on a weekend as the town is so much fun, locals are out dancing in the square, wedding parties. Enjoy your trip, J

We did Madrid, Sevilla, Granada, Córdoba. Chose this route based on holiday during our trip (NYE), and availability of Alhambra tickets.

As others have said, just put Córdoba on the way to/from Madrid, and the rest is flexible.

We did Sevilla - Cordoba- Granada. There are lots of trains to Sevilla, which I think simplifies things if you’re traveling onward after an international flight. More choices on offer. But whatever you do, make sure what yiu want to see is open on the days that you’re going to be any given place.

Is it a better choice to leave from Madrid airport and take train to Seville and just take a day trip to Cardoba? Or I was thinking maybe using Seville as a base and doing ay trip to Granada and day trip to Cardoba. Wondering if it is best to just take train to Cardoba stay a couple of days and three days in Seville. Then a day in Madrid on the way home.

Granada is really too far from Seville to be a day trip. The train takes at least 2-1/2 hours each way, and to that you must add time to get from your hotel to the train station. Then in Granada, the train station is outside the center of town. The Alhambra is not the only thing to see in Granada, and the Alhambra is a large complex, not a single building.

There aren't a lot of trains running to and from Granada. If you don't like the schedule options, you can consider a bus. The bus won't take a great deal longer, because it will take a direct highway route. The trains are extremely fast, but most travel via Cordoba, which is way to the north.

Without more specifics, particularly exactly how many nights you will be spending in Madrid and the south, it's not possible to be terribly helpful.

We saw Madrid, Segovia and Toledo. Then we went to Cordoba, Granada and Sevilla, in that order. We saved Sevilla for last because it is so spectacular. We then flew home from Madrid.

April was a very good month to visit.

No, there isn't one preferred exact route. Check google maps and/or rome2rio. Try to avoid backtracking. If Granada is your first City, make Seville your 2nd city. If Seville is your first city, make Granada your 2nd city.

If Cordoba is your first city, either Seville or Granada can be your 2nd city. On the way from Seville to Madrid or Madrid to Seville, and from Granada to Madrid or Madrid to Granada, all the trains, but maybe not the buses, stop in Cordoba.

I flew into and out of Madrid too. From Madrid I took the train to Seville the day my plane arrived, 4 nights in Seville, ALSA bus to Granada, 2 nights in Granada, train to Cordoba, 2 nights in Cordoba; train back to Madrid.

If you don't see a good selection of available hotel rooms in what you think should be your first city, see what rooms you are available if you make that city your 2nd or 3rd city.

Edit: don't try to cram any of these 3 cities into your trip as only as a day trip from either of the 2 other cities.