Spent the day in Segovia, which is an hour or so from Madrid (1/2 hour by high-speed train, then 20 minutes by bus from the train station to the center of town). The part of town we were in obviously centers on tourists, but it was cute anyway. There are about twenty small Romanesque church buildings sprinkled throughout town, most of which have been repurposed for secular ends (schools, theatre companies, etc.) so we couldn't get inside them but walked around the outsides of several.

I think the oldest non-church building in town is a 15th-century house, but a lot of the buildings, even fairly recent ones, have pronounced Mozarabic influences,
e.g. overall geometrical patterns in the wall plaster.

The oldest construction in town, of course, is the Roman aqueduct, which is really impressive. The town centers on a steep-walled ridge (like Edinburgh), which was an obvious place to put a military fort, and one problem with building a fort on top of a hill is that the troops need water. So around 100 CE, those wacky Romans found a place a few miles to the east where a fast-flowing river through the mountains was slightly higher than the hilltop, and built a channel at a steady 1% grade all the way to the fort, including a 2500-foot-long, 100-foot-high stone aqueduct (no mortar!)

across the valley

and through what are now the town walls.

The aqueduct was damaged in the 11th-century Reconquista wars, but repaired around 1500 and still in use into the 20th century.

Anyway, we walked up and down the main drag of the ridge, with side trips down twisty alleys, a fancy mid-day meal of suckling pig (for
shalmestere) and asparagus with salmon (for me), and a traditional Segovian dessert of marzipan over custard.
Found a couple of stork's nests

on top of former church (or secular) towers: apparently there were a lot of fortified 15c towers belonging to various powerful families, but Ferdinand and Isabella, in an effort to quell conflict among said families, ordered them all lopped off to a certain maximum height.
Then we toured the Cathedral, which was started in 1525 to replace the Romanesque one that had been badly damaged in a Commoners' Revolt in 1521. The new cathedral took 250 years to build, by which time the Flamboyant Gothic style in which it was started had become terribly old-fashioned, so they finished the top of the nave with a Renaissance dome

while the bell tower at 108 m was the tallest in Spain. Until 1614, when lightning struck the wooden bell tower, whereupon it caught fire and fell onto other parts of the cathedral. They rebuilt in stone, 20 m shorter than before, but still pretty darn tall. We took a guided tour of the bell tower, including the bellringer's apartment

halfway up, and our legs are still sore.
At this point it was after 4 PM. We considered going to the Alcázar, which doesn't close until either 6:00 or 8:00, but we were tired enough that we skipped it. It's a 19th-century medievaloid construction, Spain's answer to Neuschwanstein and allegedly an inspiration for the castle at Disney World.

One of the themes of this trip seems to be "expensive mistakes". I made a bunch of reservations for travel and lodging, some with the option to change and some with discounts in exchange for a "no cancellation, no changes" clause. And so far, every thing we've needed to change has been in the latter category. There are so far five (5) nights' hotel stays that we're paying for and not using. And although I thought the train tickets I had bought for today could be changed to an earlier time for free (and to a later time for a fee), this turned out to be wrong, and we had to buy new tickets back to Madrid rather than sit in the Segovia train station for three hours. I spent both too much time and too much money at a Western Union office this morning trying to send money to a musical-instrument-maker (so he can ship the finished instrument to one of the hotels we're staying at later, and we can bring it home ourselves). But at least it's only money: none of these mistakes so far has affected us physically. (Cue the Book of Job....)
Tomorrow we plan to take the bus to El Escorial (home of two Cantigas manuscripts, among other things), come back in the afternoon and get in a few more hours at the Archeological Museum.