Segovia is a very unusual town. To understand why, you need to look on the following image from Google maps.
Aqueducts remained in some European cities, but the longest preserved ancient Roman aqueduct is in Segovia.
Most of the restaurants are located near the aqueduct of Segovia, so most tourists spend their time in the evenings here. We strongly recommend to spend the night in Segovia or at least stay until dark. Here is really very comfortable, quiet and beautiful.
Most visitors come here only during the day. They all are strolling in the old town, but we started from viewpoints. To get to them, see the following diagram. There are two viewpoints, one overlooks the cathedral, and other the castle (Alcazar).
First viewpoint is easy to reach on foot or car from the aqueduct. It's a big, empty, unpaved area, that is used during the festival of balloons. It offers a good view of the old town and the Cathedral.
To get to the second viewpoint is more difficult. There are two main ways. We have been there twice, the first time through entrance 1, the second time in the evening through entrance 2.
From entrance 1 your have to walk about one kilometer. From entrance 2 you have to walk not much, but uphill. In the corner of the parking lot find stairs and use them to get to the viewpoint. If you want to make evening photos, then use only entrance 2. And be sure to have a flashlight or a phone with a flashlight, as you will need to come down from the mountain in the dark.
Despite the fact that the entrance 2 is located near the castle, I do not think that it is possible to go there directly from the castle. There is a path from the old town, you can try to find it. We walked along the main roads from the aqueduct (approximately 15-20 minutes), through the district of San Milan, it can be seen on the following map.
City map in PDF can be downloaded here.
In general, why you need to visit the viewpoint? 99.9% of the tourists visiting Segovia see the following.
And that is what we have seen.
We also flew a little using the drone.
Alcazar (Castle) of Segovia is one of the most important royal residences in Spain, the first mention of it relates to 1120. For a long time Kings of Spain lived there, but when the court moved to Madrid, the castle became a prison for two centuries. Since 1953 it became a museum. Castle can be visited, find information here (PDF).
After visiting viewpoints, we settled in the hotel (Hotel Acueducto, booking.com, 35 euros per night, 200 meters from the aqueduct) and went for a walk to the old town.
Getting to Segovia
By bus from Madrid (schedule). It is important that from 2014 buses to Segovia run from the new terminal Intercambiador Moncloa. Travel time is about 1 hour 30 minutes, bus comes almost to the aqueduct. You can also take the train C-8 from Atocha station or Chamartin station. Segovia is reachable by high-speed trains (30 minutes from Madrid and 40 minutes from Valladolid). From the train station take the bus number 11 to aqueduct.