Segovia is a small Spanish city that is a 75 minute bus ride north of Madrid. It's located in the province of Castile y León. The population of Segovia is roughly 52,000 people. But, as the title suggests, don't be deceived because for as small as it is, it packs a punch when it comes to things to see and do.
Segovia is dominated by its Roman and Christian history. You have probably heard of this charming city because of its famous Roman Aqueduct that has survived the test of time. There is a even a castle. called the Alcázar de Segovia, that was originally built by the Romans. Unfortunately, what you see today of the castle/fort has little remnants of it's Roman days. The form it currently takes is from the late 14th century to mid 16th century.
Segovia also boasts several small churches, including a stunning medieval cathedral.
Transportation
There are two ways to get to Segovia; bus and train. A bus trip takes 75 minutes or less and costs €10 round trip from Madrid. A train costs closer to €20 (maybe as much as €23 depending on the peak times) round trip. The train will get you to Segovia and back to Madrid in just 30 minutes each way.
Segovia makes for a nearly perfect day trip from Spain's capital city. There is certainly enough to do in Segovia if you would prefer to stay overnight and take your time at the different sites. I wouldn't suggest more than one night in Segovia, unless you plan to work in nearby sites outside of Segovia as well. Places like Ávila (I plan to go there later).
A morning bus to Segovia from Madrid and then a night bus from Segovia to Madrid is a great way to experience Segovia. Same for the train, if you want to spend a few more Euros on the faster mode of transportation, but the buses are comfortable enough for the 75 minute trip.
If you're not big on the idea of walking all over Segovia, they have their own bus system throughout the city but I can't speak to it. I chose to just walk.
To Do's
Acueducto de Segovia
The focal point of any trip to Segovia. Make sure to walk through its famous arches. Make sure to walk up to the viewpoint ("Mirador") above the tourism office for good pictures and views. I also highly recommend walking along the full length of it (up the hill across from the tourism office and around the bend through the neighborhood). At its beginning up the hill and through the neighborhood you can actually get on it and see the path in which the water took in the days of the Romans 2,000+ years ago.
Alcázar de Segovia
This castle was a Roman castle that was then used by the Moors and then retaken by the Christians. The Roman version hasn't survived but it was first mentioned as far back as the early 12th century. Make sure to go up the tower if you can. It's a thin spiral staircase so if you are unhealthy, maybe skip it. If you have knee problems or claustrophobia, you might want to skip it too.
The entrance fee is €9 and you will get an assigned time to go up the to the Tower. The rooms of the Alcazar well preserved and they have incredible artistic value. As it was once a fort it also boasts an Armory which is super cool.
Catedral de Segovia
This stunning medieval cathedral was commissioned in 1523 but wasn't finished until 1768. It features much of what you'd expect from a medieval cathedral. Other parts that are worth a visit is a guided tour up the bell tower. The tour will be in Spanish but your first stop will be a 360 degree video of the history of the bell tower. The audio is also in Spanish but the video does have English subtitles. After the video you continue up the tower to the living quarters. Finally, you'll get to the actual bell tower that has amazing views of Segovia and it's surrounding areas. The old bells (several hundred years old) are also totally worth seeing. Skip the bell tower if you have claustrophobia and are not in condition to go up a thin spiral staircase.
Another part of the cathedral worth seeing is in the basement. There is a room that can be accessed by following the signs (it's well marked) that features a few stunning religious paintings.
A ticket including the guided bell tower tour costs €7.
La Juderia/Cementerio
This area of the city is the Jewish quarter. It's just outside the original city walls which means you can walk along the city walls which is neat. If you continue down into what will increasingly appear to be a park (it is!) and under the roadway at the slope of the hill, is a medieval Jewish cemetery that has been excavated. After you're done admiring the cemetery's excavation site, continue up the hill. When you get to the top there isn't much there so follow the walking path to the right (towards the Alcázar de Segovia). You'll reach a bench were you can sit and rest for a few minutes while enjoying the view of the famous castle/fort.
Other churches
If you choose to traverse the city by foot, you can pop around to all the different smaller churches. Many of them may not be open but they're still neat to walk around and admire from the outside.
Things I Missed
Mirador de la Pradera de San Marcos
This is a grassy area down the hill from the Alcázar de Segovia that apparently will give you incredible, photogenic, views of the famous castle/fort. I missed out due to time constraints and since it is bit of a walk and I hadn't figured out the bus system.
Monestery of Santa María del Parral
This is one fo the top things to do in Segovia. The monastery is in the hills behind Segovia (you can clearly see it from the viewpoint outside the gates of the Alcázar de Segovia). You'll likely need to figure out the bus system to get there. Walking there seems a bit ambitious.
Iglesia de la Vera Cruz
This is also one of the top places to visit in Segovia. This tiny church dates back to the very early 13th century. A trip to this church could be packaged in with the mirador and the monastery.