Hi Nigel, You can definitely get up close to the aqueduct, in fact, there are stairs that take you up towards the top on one end. My family was in Madrid for the last week of June 2015, and temps were already around 80F, but nowhere we visited was very crowded that week. We did two day trips: one day to Toledo and the second day was split between El Escorial and Segovia. We have friends that live near Madrid who chauffeured us around, and I'm sure it was only due to their local knowledge that we were able to see both El Escorial and part of Segovia in one day. We did not have time to go inside the Alcazar Castle in Segovia, so I can't comment on it except to say it looks impressive from the outside.. I will recommend the food at Meson de Jose Maria - it was excellent - we had the roast suckling pig since there were 8 of us at the table.
If I had been traveling on my own, I would have wanted a separate day just for Segovia and spent the night there. Then I would have combined the Valley of the Fallen Monument - which we also didn't have time for - with El Escorial on the way back to Madrid.
Toledo is definitely worth a whole day, but be advised that it has some hilly streets even after you take the escalators up to the old city (or maybe I just have old knees!). Our friends told us about a State run hotel (Paradores they are called) that is on the hill across the river with a fantastic view of Toledo - I have no idea on the pricing, and only mention it because it sounded like a lovely place to spend the night - just in case you end up planning a stay in Toledo.
Rick has an episode on Toledo/Segovia/Salamanca, and then El Escorial and Valley of the Fallen are covered on his "Majesty of Madrid" episode.
Darn, now I'm wanting a bocadillo de calamares (fried calamari sandwich) from Madrid!