1 to 1 1/2 day long trips from Madrid and back-recommendations

I would still fly out of Madrid.

For a nice relaxing finish to the tour, I would head to Segovia. Short train ride, you could spend Monday night still in Segovia if you have a later flight. Segovia has a nice array of unique dishes and restaurants, nice older town with an Aqueduct and a Castle, plenty of relaxing scenic walks.

Which airport in London do you need to use or will any of them work?

I'd prefer Luton or Stansted. Heathrow as a last resort. Gatwick is too far. Relatives live about an hour north of London so LTN or STN would be great. Easyjet and Ryanair fly to both of them. Familiar with those airlines and am OK with flying them.

I agree about Segovia, you could do a day trip there or an overnight. The cathedral is good, so is the alcazar at the far end of the town, but the "wow" experience for me was the aqueduct. It's a pretty city with nice walks and plenty of places to eat and drink. I think there's rail service to Madrid.

A more ambitious goal might be Cordoba, a couple of hours by train from Madrid, worth at least two nights. You might be churched out, but the Mezquita is unique. The Jewish quarter is right beside it, and the river is also very nice. Nearby is a neighborhood filled with patios open for visiting, should be beautiful in May. You'll get a taste of Andalucia and the Moorish influence in Spain that you wouldn't get in Barcelona or Madrid. But you'll probably want to return to Madrid for your flight to London. There's good bus service between Atocha Station and the airport.

I agree with Dick. Cordoba would be a great location, and the Patio Festival is in May. Here’s more details:

https://www.turismodecordoba.org/-en-1-1

The festivals in Spain are a lot of fun - definitely recommend trying to be in a town if there’s one while you’re there.

I agree that Segovia is an amazing day trip, or even an overnight. Also agree that Cordoba is quite special, but if you go, please spend at least a night and preferably two or three. There is a lot to see in Cordoba. The patios are exquisite and The Mezquita is unlike anything I've seen. It is a church, of course, but I'd never be too "churched out" to visit the Mezquita (and I will admit to skipping the cathedral in Segovia because I was "churched out")

Either of the two places would work. Both are about 2 hours by train from the main train station. I would plan on flying out of Madrid since there are direct flights on RyanAir to STN and many airline to LHR. Sounds like a fun trip.

ALVIA and AVANT trains from Madrid-Chamartin Station make the run to Segovia in 27 minutes.

Looks like we would be there during the time of the Fair of Cordoba. That sounds like it could be fun. We could get on a train from Madrid Sunday morning, and leave Cordoba Tuesday. Looks like we could get flights to the UK from either Madrid, Seville or Malaga. Price and timing seem similar. Madrid is farther away. Any advantage/disadvantage of flying out of Seville or Malaga?

I haven't been to either of those airports, but I believe there are more flights from Malaga, and fares currently look lower from Malaga. On the other hand, there's more-frequent train service to Seville. On the third hand, there's a train station at the Malaga airport. It's served only by local trains (Cercanias), so a transfer would be required, but it appears that those trains are frequent. It's Line C1.

I have flown on Ryanair from Sevilla to London Stansted. No problems, just be aware they are a budget airline and follow their guidelines. Price is reasonable even if you have to pay to check a bag. Sevilla airport is small. I used to live in the UK and flew on Ryanair multiple times. I just flew with them in September from Poland to Sicily with no issues. Sevilla would also be a great two day destination. Either Córdoba or Sevilla will give you a taste of Andalucía.

Should you decide to opt for Segovia and then fly out of Madrid, I have a suggestion to add. Not far from Segovia is the Royal Site of La Granja de San Ildefonso. It is a beautiful royal palace with lovely gardens and grounds. Reachable by bus from Segovia.

I have been trying to think of some other options that are not traditional destinations, that would be great for walking around and exploring and just enjoying the place. Trujillo is a wonderful small medieval town not too far from Madrid in Extremadura. It is filled with narrow alleyways, a castle, and a central plaza that is almost haunting at night. I think you would have to travel there by bus as it is not on the train route. It is like stepping back in time to Middle Ages. I very much enjoyed it. Also in Extremadura, but accessible by train, is beautiful Cáceres with its gorgeous Old Historical Center. From either of these two destinations you would need to return to Madrid to fly on to London.

We stayed a night in Malaga; it was our original ending city for our Spain trip but the flight was changed to Madrid. If you leave them there, the center of the city is a great spot for your last evening.

I would be frustrated to only be able to spend one night in Sevilla.