Although it was said of Granada, not Segovia, I would echo the words "Give something to the poor blind man, because there’s nothing crueler in life than to be blind in Granada." Equally as unjust it would be to be sightless in Segovia. You can’t miss the aqueduct. I highly recommend starting up the road that passes by the Hotel Acueducto at the "starting" point of what’s left of the structure. I brought a group of high school student here in 2004, and we walked from the train station purposely to this point first. When we got to the six-foot high structure, the students were noticeably disillusioned as I told them, "Here it is. Isn’t it great?!" As we walked the length of it and turned that last corner, though, the jaw dropping made it all worthwhile!
The self-directed walking tour is easy. Just walk up the calle Cervantes to the Plaza Mayor and find yourself at the cathedral. Gawk, jaw agape, at the splendor, and then move towards the Alacazar. As you walk note the narrowness of the streets, and how they’re all one-way now. Think what it must have been like just fifteen years ago when cars could come and go on many of these old streets in either direction. There was then, and still is now, only one traffic signal in the old part of Segovia.
There are two things left to see in Segovia once you get to the castle. After "doing the tour", I recommend you look off to the north and below. You’ll see a little church on the outskirts known as the Vera Cruz. Visit it and see the Romanesque bell tower, partial extant frescoes on the walls, and out front, according to the caretakers, the erosion-induced unearthing of bone fragments of those buried in the church yard during the bubonic plague. Legend always outpaces fact for interest level. The second thing you should do with time is to walk, don’t drive, the 1k to Zumarramala. That’s the little town on the "horizon" up the street from Vera Cruz. There’s a plaque on the first building you’ll see there that, in essence, reads "I know of no one who, having come to this place, has not been conquered by its unmatched beauty." Truer words were never spoken. The castle at this point looks like the gargantuan bow of an Herculean ocean liner. Take your time. This is something that was more than 500 years in the making. Give it a few minutes at least!