I totally agree with WJW2. Segovia is a magical city. It's like walking through a time machine...
You might want to take the bus, La Sepulvedana,their terminal is at Paseo de La Florida 11.
whether you come by train or by bus, be sure that you take either a bus, or a taxi to the Aqueduct.
To me it's the perfect daytrip from Madrid. You can spend a leisurely day and see a lot of spanish history. I suggest you dine at Meson de Candido, one of Spain's oldest restaurant, famous for their cochinillo asado, its so tender they have an act where they cut it with a plate!
Of course, the Aqueduct is breathtaking, and I was told that it had been used up to the 1970!
Those Romans built well!
You proceed up a broad avenue and to the Plaza Mayor, very small, but charming, there you'll find lots of wonderful ceramic tile souvenirs.
Next to the Plaza is the Cathedral, a stunning edifice, which has a great museum. continue up and you end up at the Alcazar, oka as Cinderella's Castle in Disney World
From the Alcazar, you look down into a small valley where you find the Vera Cruz Church, constructed in the 13th century by the Knights Templar!
Anyway, in my opinion a great place to visit in a day!