There are several hundred underground cities in Cappadocia region. The most suitable for the visit is the town of Derinkuyu. It was discovered in 1963 and in 1965 opened to the visitors.
The city was built probably in VII-VIII centuries BC. To better understand its dimensions, it is enough to say that the maximum depth of the rooms is 85 meters! More then 20000 people with their livestock could live underground the same time. Moreover Derinkuyu was connected by a 8 km tunnel with another underground city of Kaymakli, but now it's swamped.
City has 13 floors with ventilation shafts (8 are opened to visitors), as well as 15,000 small mines that hold air even at the lowest levels. Were found kitchens, dining rooms, wineries, stables, warehouses and even corrals, churches and schools. I can not imagine how it could be built. And why? It is believed that this is a temporary shelter during the war. It is still not known exactly who built it.
The city was well protected from possible invaders. In case of danger, moves to the dungeons were closed with huge boulders, that can be opened only from inside. Even if the invaders were able to get on the first floors of the city, it was very difficult to find the correct way without knowing the secret passages and labyrinths. Sometimes they even could not find the way back to the surface. There is a view that the tunnels were built in a such way to confuse intruders.
In general, I must say that the unprepared tourists (like we are) will be scared inside. The deeper you go down the more terrible you fill. After all, the city is many thousands of years old and reliability of ceilings in serious doubt. We will not be surprised if some visitors can begin to panic at a depth of 50 meters under the ground.
There is an episode of the documentary series Ancient Aliens (season 2, episode 4) about Derinkuyu.
Getting there: From Nevşehir to Derinkuyu, buses start at 7:30 and run every half hour. The last return bus is 19:00 from Derinkuyu to Nevşehir. This bus is about 40 minutes and costs 5 lira. On Sunday it only runs on the hour.
Nevşehir has an airport, where fly Turkish Airlines, Onur Air, Pegasus and SunExpress. Bus station from the airport can only be reached by taxi. Several bus companies have direct buses Istanbul - Nevşehir:
http://www.nevsehirlilerseyahat.com.tr
http://www.metroturizm.com.tr
http://eticket.ipektr.com/firms_68/Default.aspx