Day or side trips from Madrid?

Popular day trips include Segovia (Alcázar and Roman aqueduct), Salamanca (University town), and Alcalá de Henares (Miguel de Cervantes’ birthplace and writer of Don Quixote). Cuenca (cathedral, gorge, and hanging house) is also a possibility. Not as easy to reach. Some people stop in Ávila en route to Salamanca. Its main draw is the wall and towers surrounding the town and there are no other must see sights in the town. It can be seen in a couple hours.

You couldn’t adequately see Sevilla or Granada with the time you have.

Cordoba is a 2 hour (one-way) train ride from Madrid. Not as close as Segovia (which is what I would recommend), but throwing it out for consideration.

The old university town of Alcala de Henares is easily accessible from Madrid via a frequent commuter train. It's a cheap side trip, and the historic center is very pretty.

Cuenca isn't terribly hard to get to, but at this point it might be expensive. The town is on the AVE (fast rail) line between Madrid and Valencia. Those trains can be reasonably priced if you buy the tickets early, but they can go so high as to make a day trip unreasonably costly. Check renfe.com to see whether there are any reasonable tickets remaining for your date. Be careful; you don't want tickets on the slow trains; the take forever to get to Cuenca. You'd be prudent to budget for a taxi into town from the train station; there is some bus service, but I don't know how frequent or well-timed it is, and buses may be less frequent or even non-existent on weekends. Since you mentioned your sister's age, I will tell you that Cuenca is most definitely a hill town. However, you could have a taxi take you to the top of the town and then gradually walk downhill. Cuenca is a very interesting place, with hanging houses along a ravine, an old church, and a couple of small modern-art museums.

I'm not a fan of Avila at all. You will already have seen Toledo; there's just not much to Avila except the wall. I'd much rather make another trip down to Toledo (love that place).

I love Cordoba so much it might be worth the long (and possibly costly) train trip. It's the sort of place (like Toledo) where I'd prefer to spend 2 or 3 nights, but you will already have seen a lot of the sights on your tour.

Many thanks for all the prompt replies. Will look into all the suggested places. As much as I’d love to head south, it seems it would be a tease with only two days to do it. Next time 🤞🤞
Someone asked if we know who our tour director will be...not yet.

Segovia with its ancient Roman aqueduct is worth a day trip from Madrid,

We went to El Escorial which is only 28 miles from Madrid and is the largest renaissance building in the world, and a UNESCO World Heritage Site.

Salamanca is further away from Madrid. I stayed there for one night. It was lovely.

I think heading for Andalucia is not worth it given your time frame.