Madrid - airport hotel logistics?

I stayed by the Puerta del Sol in Madrid and it was very easy to take a train from there to the airport. My recollection was it was about 45 minutes and I did have to change trains. Super easy and my flight was a couple hours earlier than yours. That area is a beautiful and festive place in the evening. I stayed at Hotel Europa which I thought was a good value and well located.

We stopped in Cordoba on our way back to Madrid from Granada so I can't help you there.

You didn't ask, so forgive me if you do not want itinerary input, but I think you are short for Sevilla and Cordoba. There is so much in Cordoba beyond the amazing Mezquita. The historical Jewish quarter is stunning. Sevilla and Cordoba were my favorite cities, Granada less so, but there is the amazing Alhambra. There is a lot to do in Sevilla, more than Granada. We stayed 4 nights in Sevilla, 2 in Granada and 2 in Cordoba. As you noted, it is often cheaper, even necessary from some locations to fly in or through Madrid. If you are back to Spain, you can easily see more of Madrid. I think that Madrid is far less interesting historically and culturally than the great cities of Andalusia.

If you are wanting to take a day trip to Segovia or Toledo (IMO, Toledo is another city worth more than a day trip, however) or are really interested in Madrid's art museum that could be a consideration.

I agree that you have relatively too much time in Madrid unless you either are big art fans or have plans for day-trips. It's not that you cannot occupy yourself in Madrid (there are plenty of neighborhoods to walk around), but your time in Seville--which has a lot of very interesting sights--is going to be painfully short, and Cordoba is worth more than a partial-day visit.

Thank you both for the input. Now I'm working on day by day plans and so there's the travel day flexibility of staying longer in one place, traveling in the evening to the next, etc. So it sounds like we should try to maximize our time in Seville; I don't think we will be able to do more in Cordoba unless we stop twice (once on the way south, once on the way north); I need to look more closely as I had the impression from the guidebook that it's mostly about visiting the mezquita and walking around the Jewish quarter. I'm trying to plan a balance of activities to keep the interest of the teenagers in our group; they enjoy guided tours (both site and walking tours) and anything food-related.
Are there other sources of info you recommend re: things to do/see in Seville and Cordoba beyond the RS guidebook? Or just your own personal favorites?
Thank you!

I have done both - stayed at an airport hotel and stayed in Madrid proper (right across from Atocha). With a flight that late I'd opt for staying in Madrid. The airport hotel was OK, and there were a couple of places to get food nearby (there was a large mall with a decent food court) but nothing very good. But that flight was a lot earlier than yours. For a 1pm flight you don't need to be at the airport till 10, meaning you don't need to leave central Madrid till 9. I don't consider that at all early.

The metro from the Sol metro stop to the airport is indeed 45 minutes with changes at Principe de Vergara, then Colombia, stations. Two tickets from Sol to airport T2 were €10. Whether you stay by the airport or in town may be determined by your flight time. For an earlier flight the airport makes a lot of sense, since you can sleep a little longer and maybe have some breakfast. Our flight yesterday (before it was cancelled) was at 11:00 and we were going to leave the hotel at about 7:30 to allow plenty of time. Got rebooked through Frankfurt, so got to have breakfast at the hotel before heading to the airport around 8:15, and waiting for the 12:55 flight to Frankfurt. Had we stayed out by the airport, we wouldn’t have had to allow so much extra time, in case there were metro issues. I guess it’s personal choice and comfort level, which option you choose.

Rather than make two Metro changes, you might try the Expres Aeropuerto, a bus running from Atocha and Plaza de Cibeles, which takes about 40 minutes and serves all the terminals. I plan to use it next month, but haven't before. Easier than hauling bags between subway trains.

We took the aeroport bus from Arocha last Monday. It is 5 euro per person and does take 40 minutes. Madrid airport is very taxing to get to your gate. I think we had to show passports at least 4 times besides standing in line for checkin. Then after going through security ., we were required to take a tram to our section and then a 12 minute wqlk to our gate. We left our Madrid hotel at 8:30 in a taxi to Atocha. Arrived at our plane at 11:35 for an 11:35 flight. Allow plenty of time. Stressful morning!

Thank you so much for the tip re: the bus and also for the info on how long it all took - WOW, I guess I'm used to a different timetable as I would have thought leaving 3 hours early would allow for a lot of cushion ... Will be careful about that.

We took the train to the airport, not the metro. In fact, I don't believe we took the metro at all in Madrid. We had been advised that the train system was much easier to use than the metro. We left from Puerta del sol and I am pretty sure that it was just one train change. It was easy.