No shortage of taxis anywhere in Spain at bus and train stations...don't worry about that. I suggest you take the bus over the train (to Segovia) for reasons discussed in another similar thread.

For the more adventurous (and late arriver) consider hiring a taxi for the trip to Segovia...sounds loco, but if you absolutely don't want to stay in Madrid that night, it's a viable option. Set a price prior to leaving, though, and get the driver's info (you'll have time on the drive up). I taxied from Segovia to Avila years back, and remember it being reasonable, especially since you'll be getting door-to-door service.

Hey this is getting crazier and crazier but I'm sure we're keeping some people entertained.
In an ideal world I would go to Segovia on Friday night, so if I did decide to take a taxi, does anyone know what the maximum I should expect to pay would be (I won't have much luggage)? In fact, as I mentioned before, I need to go further than Segovia (and this is where it gets crazy because I have visions of myself driving round mountain cliffs in the Spanish night trying to make myself understood to the taxi-driver with my half-forgotten Spanish), specifically a place called Torre Val de San Pedro which is at the foothills of the Guadarrama range, near a village called Pedraza. It is 115 kms from Madrid and 27kms from Segovia and is 1120 m above sea level.
CaliBasco thanks for your suggestion. By the way, do you mention getting the taxi-drivers details as a safety precaution (difficult when I'm already in the taxi!) or so I have more leverage when it comes to paying at the end?