For me, the Cathedral of Segovia is the best sight in the city, even more so than the Aqueduct or Alcazar, which are both amazing in their own right. The Cathedral, though, has something special. It's a combination of the sheer size, the never-ending geometric detail of the domed ceilings, the dozens of ornate chapels and altars lining the walls, the soft light passing through the stained glass windows, and the holy quiet. It's overwhelming and upon entering you understand the biblical meaning of the word "awesome."
The place fills up quickly around 11 or noon with (often noisy) group tours, so make sure to try and get there first thing in the morning. Photography of all kinds is prohibited, but no one's really watching so you can snap away without your flash. If not, just take the visit slow: check out the small details in the chapels, enjoy the towering spaces, and sit a while in the choir area.