Is there a preferred order to visiting Spanish cities?

Whichever minimizes travel time. Each city is unique in its own way so it really doesn’t matter which you visit first. I would do Toledo at the same time as Madrid since you need to go through Atocha station to go to Toledo.

Since you don’t want to go from Granada to Madrid, a logical order is Granada, Sevilla, Córdoba depending on public transportation schedules. I can’t help with that because I always have a rental car.

Maybe you are overthinking this? Either Sevilla/Granada/Cordoba or Cordoba/Granada/Seville will be fine, there is no "best" order for these three cities, geographically or aesthetically, there are all equally interesting in their own way, each has their own "wow factor" site, Sevilla Cathedral, Cordoba Mezquita, and Granada Alhambra.

When I went I did Sevilla, Cordoba, Granada.

You could also consider our very modern and comfortable ALSA buses to travel from city to city, like from Granada to Madrid, if they have a better scheduling. I know that Americans only want to travel by train in Europe, but in Spain our buses are just as good.

There is no smooth direct route you can travel, without at least some backtracking. For example, right off the bat, when done in Toledo, you backtrack to Madrid to get anywhere. Cordoba and Seville are then in a line, but to get to Granada from Seville, is either a train through Cordoba, or a direct bus.

You might consider Toledo-Seville-Cordoba-Granada-Madrid.

Even Granada to Madrid has several routes, but there is a direct train.

In the end, pick one, the only penalty is maybe an hour or two of extra travel total, Nothing much to worry about.

As you've already realized, there's not a lot of rail service into and out of Granada. I'd position Granada where it fits best, logistically, then do whatever you like with the other two. Or, as already mentioned, consider buses into or out of Granada. Trains are by far the fastest choice along the Madrid-Toledo(back to Madrid)-Cordoba-Seville route.

By train you can slot Cordoba between Granada and Seville. I don't know whether that would work as well if you were entering or leaving Granada by bus.

Dawn,
When my mom & I visited Spain, we took the train to Córdoba on day of arrival, then took the ALSA bus to Granada. Then another ALSA bus to Sevilla, and finally a fast train to Madrid and ended our trip in Toledo.

We’d visited Madrid & Toledo (as a day trip) on a previous trip and had promised each other that we’d spend a few days in beautiful Toledo.
All these cities are wonderful but our favorite became Córdoba.

Wishing you a wonderful trip!

HA HA! Oh, no doubt I am overthinking this, but that's me! lol

It's good to know that all of the cities are unique and will all have their own wow factor. I will take another look at both the bus and train schedules and figure out which times work the best. Right now I'm thinking this order: Toledo (2 nights), Seville (4 nights), Granada (3 nights), Cordoba (2 nights) and ending in Madrid for my final 4 nights.

Thanks everyone for your thoughts - I really appreciate it! And @History Traveler - thank you so much for the María Rosa Menocal's Ornament of the World recommendation. I can't wait to read/watch it.

Yes.
You should always travel clockwise vs widdershins .

Each city is unique and very different from each other architecturally, visually, and with its own special ambiance. And each city has equally awesome and equally important sites. I loved every place we visited but my favorite is Seville. What makes the most sense to me are the train and bus schedules. We flew into Madrid and home from Sevllle. This was our order which worked perfectly for us:

Madrid, Toledo, Cordoba, Granada, Malaga, and Seville.

Because you are flying in and out of Madrid, it makes sense to visit Toledo first and Madrid last. From Toledo, you can go directly to Granada, then Seville, and then Cordoba since it is closest to Madrid.

Regarding transportation we used the trains and the ALSA buses. The buses are clean, modern, air conditioned and on time. Choose the schedules that work best for you.

I don't know if there is a bus connecting Toledo with any of those cities, but since the Toledo train route requires you to return to Madrid, I would consider going to Cordoba next since it is a shorter transit on a travel day. Then Granada, then Sevilla (which has a fast train back to Madrid for the last leg).
They are ALL spectacular, enjoy!

The last time I looked, taking the fast train back to Madrid from Toledo, then heading south to Cordoba/Seville was the best way to go. I wasn't able to find any direct buses from Toledo south. Despite the extra mileage caused by doubling back to Madrid, it's not a terribly time-consuming trip, because the trains are quite fast.