The small city is a perfect day trip from Madrid, and has such a different feel from the busyness of Madrid. A 27 minute Acela train ride from the Chamartin station in north Madrid (get there by Metro in minutes from the center of Madrid) takes you to the Segovia station and a well-timed bus takes you to the old city center. The aqueduct is magnificent and it greets you as you step off the bus. There is a great TI right next to it, for maps and advice, and a stroll along the narrow streets full of restaurants and shops take you to the Plaza Mayor and the cathedral. A short walk from there to the Alcazar (and its amazing views of the countryside), then an easy walk back to the city center. It's a lovely city, very quiet, charming. Worth a day trip for sure.
Anne, I couldn't have agreed with you better. So many times, some vacationers include only Toledo on their list of short trips from Madrid and forgot Segovia. I think Segovia should be as equally as important as Toledo for a day trip destination out of Madrid.
I think Toledo has more worthwhile sights than Segovia, but I agree with the OP that Segovia is a great day trip -- and, unlike Toledo, you can pretty much "cover" it in a day. The aqueduct is in one of my top half-dozen or so "wow" sights in Europe.
Segovia is great (as is Toledo). I had to see the aqueduct. Also, found the castle amazing. In my opinion, both Toledo and Segovia are must see places if you go to Spain.
The aqueduct is about 1800 years old and until the 1960s still carried water. The Romans were great engineers. Also, there is another amazing Roman aqueduct in SE France called Pont du Gard that is worth seeing.