day trip to Segovia from Madrid

In 2014, we were taken to this restaurant for a 2 hour lunch by locals to have the regional dish suckling pig
https://restaurantenarizotas.es/

The obvious things you will see in Segovia is the Roman Aqueduct and the cathedral.

But on the way to Segovia from Madrid we also stopped at El Escorial
https://el-escorial.com/

The castle on the far edge of town is worth seeing. At least from the outside

It's a pleasant day trip from Madrid. I used the train. Going, I took the direct slow train from Atocha. It drops off at on station. Follow the locals to the bus for the trip into town. Returning, I took the faster train that requires a transfer. That is from a larger train station and has regular shuttles. If going in cooler weather, know the station is completely concrete and may be quite cold if there is a long wait foe the train. I recall Rick covering how to do it by train.
There is a main street towards the castle. It is a shopping street and the one the tours take. Take the parallel road on the left for a trip through the old Judaism part of the town. More interesting and much less crowded.
There is a tourist info centre just under the aqueduct with a guide map and the 'must sees'.
If you have no hesitation to do so, do plan for the suckling pig and the local ponche Segoviano (cake).

The castle on the far edge of town is worth seeing. At least from the outside

The Alcazar! The ceilings alone are worth the price of admission!

Scudder, I agree, the interior of the Alcazar was lovely as were the views from it. However, as far as I'm concerned, it is an absolute must to at least walk to the edge of the town to see the exterior of the Alcazar and the countryside views. It seemed to me that most people stopped at the main square/cathedral.

The 1882 rebuilt Alcázar (due to fires) is worth visiting. Of course you can’t miss seeing the aqueduct. A restaurant famous for cochinillo (21 day old roasted pig) is Mesón De Cándido. it’s on the main plaza near the base of the aqueduct. In all my visits to the city, I’ve yet to visit its cathedral.

On my first trip to Segovia in 1978 the aqueduct still carried water to the city and we drove between the aqueduct arches. By 1980 one could no longer do that.

My best memory of the Alcazar is the fortifications and the sheer cliffs. (There was no way that lost Tilley hat was going to be retrieved).
The major fire of 1886 means a lot of the ceilings are actually restored. Like many sites that started over 1000 years ago, you need to peel back and recognize the different centuries of 'improvements'.