Madrid - Segovia

It's easy and fast to get between Madrid and Segovia by train. I wouldn't do a bus.

The trip to Segovia by train is quick and very easy. From the Segovia train station, you take a bus to the old part of town and passengers are dropped off right at the aqueduct. There is a 30 minute train which I took, be careful when you book the tickets, there are some slower trains. Segovia is a very interesting little town, I would make sure to walk all the way to the Alcazar for great views. Along the way, Plaza Mayor and the cathedral is quite impressive. I would suggest using RS's walking tour of Segovia, including the stop for the delicious dessert at Limon y Menta, the dessert is a custard and marzipan cake. I do not think you need a tour, it is so easy to visit on your own. However, if you want to do some comparison shopping in terms of getting a private driver, your train tickets will be approximately 22euro round trip per adult, depending on when you buy the tickets and I believe the bus from the train station to the aqueduct is another 4euro round trip. I do not know if there is a discount for teenagers. I can't help with a VRBO for Madrid, but I stayed on the Puerta del Sol. It was convenient to transporation and the neighborhood was walkable at night, and easy walking distance to the royal palace (which is lit at night along with some other buildings). There is also a bus from Madrid to Segovia, but I don't know much about it except that it takes longer but, it does drop off closer to town (it might be about a 1/2 mile walk)

I took the bus. Here's how:

Buy your tickets online so you don't have to queue at the ticket office.

Take the metro to Moncloa Station. Navigate to the bus stop (involves a flight of stairs, if I remember correctly). Look for the correct gate of your bus. There are monitors at each gate that will update as it gets closer to travel time. You'll likely see fellow tourists queuing.

The bus is slightly cheaper than the train and it stops very close to the town. We walked about 5 minutes to get to the aqueduct.

Quick Googling tells me that the bus from Madrid to Segovia takes about 2 hours (assuming no traffic disasters, I guess). Jules is right that there are trains that will get you there far faster--in less than 30 minutes. On a short vacation, the difference between a 1-hour round-trip and a 4-hour round-trip is substantial. [BAD INFO: In addition, it may be quicker to get to Atocha Station from the poster's lodgings than to Moncloa bus station. The latter has Metro service, but they may be within walking distance of Atocha. Nope; the Segovia train departs from Chamartin Station.]

As far as VRBO's in Madrid, the legal ones that are used for holiday lettings should have a registration number starting with VT-XXXX where the X=numbers. Any place in the center part of the city is fine though with 9 people you may need to find two or look out farther for a bigger place as Madrid apartments are small compared to American ones-unless you live in NYC.

The train to Segovia leaves from Chamartin Station, not Atocha Station. We stayed next to Atocha and the time difference between getting to Moncloa+bus compared to getting to Charmatin+train+bus wasn't that great.

Rats; I knew that! I'll correct my earlier post.