Fall trip to Malaga

I would not stay that far from Malaga. As I recall, it is not a particularly attractive area, there are few attractions and areas of interest, and to do your trips you will have to get to the train station or bus station on the far side of Malaga. It is not near the airport.
Anywhere west of Malaga (eg Estepona, Gib) is not on the train line.

I'd stay in a quiet area of Malaga itself, near the beach on the east side if you want beach.

I consider El Palo a great and authentic base for relaxing. Which is famous for its seafront chiringuito, and for that a perfect example is El Tintero. Before your bookings you must be sure about if the second-floor apartment has an elevator because for your parents in their 70s and 80s it is a big challenge to go upstairs.

El Palo is a 30 minute drive from the airport or close to an hour using public transportation. It is 30-35 minutes from Málaga center city by bus. For me, it would get really old very quickly going into the city from El Palo or for taking the side trips you are considering. You won’t get to Toledo or Madrid as day trips as they are too far away.

Cueva de la Pileta won’t be easy to reach using public transportation. Even if it is, the bus schedule may make it impractical. For the cave day and Ronda consider renting a car. Also, check the cave’s hours since it has somewhat limited open hours.

Using public transportation I feel your plan is overly ambitious, especially if staying in El Palo. You want to visit a number of places as day trips when they merit an overnight at a minimum.

If all you want to do is hang out and not see Spain, then El Palo would probably be fine. You’ve thrown out a lot of ideas, but I don’t think you’ve thought much about the time involved executing the plan.

"Before your bookings you must be sure about if the second-floor apartment has an elevator because for your parents in their 70s and 80s it is a big challenge to go upstairs."

And don't forget that Spanish 2nd floor may well be US 3rd floor.

Also check if it has heating. Some beach apartments are only designed for summer use.

I was just in Malaga and love the city and the whole area, so that sounds like fun to me.

If I had to offer another idea, what about the Huelin neighborhood southwest of the port? It has a lot of good restaurants and a nice beach, but it's also closer to the airport and train station, with a subway stop.

I also recommend Nerja as a day trip for Malaga. The beach is quite nice and the cliffs are beautiful.

On Google street view that area looks really cool and interesting. Assuming it's relatively safe, I believe I would really enjoy staying there.

To me, part of the appeal of travel is putting yourself into areas that you are "out of place". How many times can you go to xyz museum, or castle, etc, etc, etc? The proximity to tourist or over crowded areas is not necessarily a concern.

Also, check out the food at this particular place, in the neighborhood, it looks amazing. I get excited just by looking at it.

I have a month in Malaga coming up and chose the area around the train station. It isn't as noisy as central town particularly through Carnival.
I also looked west of town on the local commuter train route. Lots of Expats there and also newer builds.more likely to have heat or elevators.
Keep in mind 'heat' may not be listed, but if the have AC via a split, then chances are there is heating....just not a separate heating unit. Message the host to verify or read reviews for the time of year you are going.
I know someone in thr forum recommended Rincon de la Victoria but he wasn't doing daily commutes to Malaga. But when he did he said it wasn't too onerous.
If it wasn't my first visit to the city, I would be looking at something east or west but connected to trips in maybe twice a week.