Many tour groups will try to shove Segovia together with Avila/Valle de los Caidos/El Escorial. This is an injustice to all of these places, but for people like you and me, time is of the essence as well.
Avila is a bit further out than Segovia, so what I recommend is doing the rental car thing. Go to Avila in the morning (if you go EARLY, you can catch the light of day on the walls...truly amazing), poke around the walls, the cathedral, "Cuatro Postes" on (what used to be the) outskirts, see Santa Teresa de Jesus' convent, then head for Segovia.
You should get into Segovia in the late afternoon/evening (it's about an hour+ drive), and then be able to partake of the ambience there, while seeing the walls and aqueduct alight. They truly are more beautiful at night, and completely accessible. Have an awesome dinner at one of the fine mesones in Segovia, and get a good night's rest...wake up and sightsee the incredible array of churches, including San Lorenzo,
San Millán and
Vera Cruz , along with the
cathedral , not to mention the Alcázar.
You can expect about a four-hour drive from Segovia to Burgos (although it may take you less time...I always allow for that little out-of-the-way castle or monasterio...). Anyway, there are threads on where to stay and what to do in Burgos already on this site.
Make your way back to Madrid, and make Toledo a day trip with Madrid as your base. Again, there are comments on Toledo all over this site as well. Just be glad you're not sucked into only going south of Madrid. Burgos is absolutely incredible in its historic riches, but suffers from no press (and no beach). Enjoy your odyssey!
[This message has been edited by Antonio (edited 01-31-2001).]