Segovia is beautiful but in November it can get really cold; It’s still a lovely day trip from Madrid. Bring a coat and scarf and catch the Sepulveda bus from Madrid’s Estación Príncipe Pío. If the ticket window isn’t open then you can purchase tickets from the machine at the end of the hall usually next to where you’ll board. The bus ride is a little over an hour but comfortable and the time passes quickly. When you arrive at the bus station you are only a few blocks away from the tourist center and the main attraction, the aqueduct.
If you want to take a tour of the city, there are walking tours with a guide, self-audio tours and a tour bus. We purchased the mp3 player audio tour guide for 5 euros (per until the end of your stay). It was great! You could go at your leisure or skip around and still learn all about the history of Segovia and the incredible architecture. The audio guide also comes in a few different languages. Well worth the 5 euros if you stay for more than one day.
Among other sites, we visited the Alcazar. It costs €4.50 for general admission, + €2.00 to visit the tower of Juan II (great view but could be hard on the old knees) and an extra €1.00 for a guided tour in Spanish (the guide was great and cracked jokes the whole time).
Segovia is a wonderful little town for a daytrip. I hope to go back in the springtime when it is a bit warmer because there are more walking trails around the city and I heard you can rent bikes for 3 euros a day. What do you suggest for a daytrip to Segovia?