I had no intention of visiting Segovia, but I met some people in Madrid who were originally from Segovia, and they invited me there with them for a night. Gladly, I went along.
Segovia is only about an hour's bus ride (€6, one way) from Madrid's Principe Pio station. What a beautiful city! No wonder my new Spanish friends take the weekend to go home.
Highlights include the aqueduct, built by the Romans 2,000 years ago, the cathedral, and the castle. It's a rather touristy town, so you'll find more than enough souvenir shops and the like. There's a tourist information office right by the aqueduct.
My friends get tired of going out in Segovia, because, they say, it's always the same bars, same people—typical of small-town life. So, it seems that while the town is touristy by day, the nightlife stays fairly local. Indeed, I only met two Americans, and they were living in Segovia for the summer to work on their Spanish.
If you have a spare day, Segovia is worth a stop.