Is it worth the day trip from Madrid?? If so, what is best to see?

Yes! The Alcazar the Cathedral, the Aqueduct. If you go on a tour bus, do not take the Gastronomic tour! I've found that such tours don't take you to the best restaurants and they 'short ration' you on just about everything (including wine). Find el Meson del Duque (up the hill from the Aqueduct) and have the Cochinillo asado (roast suckling pig) or the Corderito asado (lamb). I recommend a bus tour because you have to drink red wine to take away the greasy aftertaste and you don't want to be driving after drinking ...

n_marquis,
Another yes! It's a lovely and very walkable small city, one of my favorites (all the S cities are my favorites). NED has given you the highlights, the big 3 sites not to miss, which you can easily reach by foot, starting out in the Plaza del Azoguejo where the amazing aqueduct looms above you. To reach the cathedral simply walk up the pedestrians only street, Calle Cervantes, which becomes Calle Juan Bravo as it reaches the Plaza Mayor, where you'll find the Cathedral. (You'll pass Mesón Duque on your left; one of the 3 legendary "hornos de asar", roasting taverns, for that suckling pig/roast lamb feast-the other two are Cándido at the Aqueduct and José María, just to the east of the Plaza Mayor).
Then from the Cathedral just follow the crowd down the long, narrow Calle Daoiz to the Alcázar. Until Nov. you'll have a chance to see a wonderful special (and free!) exhibit in the Cathedral, "Las Edades del Hombre", sacred art (religious sculpture and paintings), the treasures of Castilla-León. It's quite impressive-but closed on Mon.
www.lasedades.es

I take the "La Sepulvedana" bus from Madrid to Segovia, which is comfortable, easy and cheap, if you'd rather take public transport rather than an organized tour. The busses depart from Paseo de la Florida #11, next to the Hotel Florida Norte (take the metro: Príncipe Pío, grey circular line #6, then cross the street to the station). There's express bus service with departures almost every 30 min. during the week (a few departures have 3 intermediate stops). Trip takes 1 hr. 15 min., flat. You need to purchase your ticket before getting on the bus, and you'll be given an assigned seat. I take the express at 9 (daily) or 9:30 a.m. (not on Sun.) There's also a daily 10 a.m. express. From Segovia, the last return bus leaves at 8:45, Sun. at 10:30.
From the bus station in Segovia on Paseo Ezequiel González, walk down to corner and take a left onto Avenida Fernández Larreda, past Kitius, a computer store with Internet access and continue on, and it becomes a porticoed, pedestrian only street. It's a pleasant, easy 10 min. stroll to the Aqueduct and tourist office. No need for taxi.

Segovia is well worth a trip. It is a well-preserved city with many striking buildings and monuments, the most famous is the Roman Aqueduct that is still in working condition almost 2,000 years after its construction. You'll love the Alcázar, a medieval castle, and the Segovia Cathedral.

There's a lot to do there, with MANY tourist shops and restaurants. It is EASILY walkable and if you find steps leading up to a rooftop, you can take in some fantastic views of the Gothic/Medieval architecture and mountains not too far away. GO!

SHE'S BACK !
Please Maribel--can't you give us some more detail--like what to wear.

Segovia is well worth a trip. Just remember that the old town is actually quite an uphill walk from the acqueduct. Lots of people think that this is the old town and park there.

If you only have time for one side trip, however, Toledo is much better and much easier to reach.

The cochinillo asado at Meson del Duque may have been the best meal I had in Spain. As to whether Segovia is worth the trip, I'd say it depends on how long you have in Madrid. Only two days? Then no, I'd stick with Madrid. 4 days or more? In that case, a day trip to Segovia is worthwhile IMO.

Maribel, could you give us your personal opinion on which is the best of the hornos de asar? I hope to revisit Segovia sometime next year. Muchisimas gracias!