Basilica Cistern is located right across Hagia Sophia ( Ayasofya ). It provided water to İstanbul during Byzantine Period. It is the largest of all cisterns in Istanbul. The cistern Basilica is 70 m. in width and 140 m. in height. The dome, covering area of 9800 m2, is supported by 336 marble columns arrenged in 12 rows each consisting of 28 columns ( 9 m. height ) placed at a distance of 4m 90cm. from one another.
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Constructed in the 6th century during the reign of Emperor Justinianus, the most prosperus period of the East Roman Empire. The water reserved in the cistern was transported from Belgrad forest by Emperor Justinianus which is 19 km. form the city. In the 1985 the Metropolitian municipality of Istanbul undertook the restoration of the cistern . On the 9th of Septemper 1987, it was opened for visitors as a vitalized example of universal cultural heriage.

The Basilica Cistern is located too closed to Hagia Sophia ( Ayasofya ).
How to go Hagia Sophia ( Ayasofya )?
You can go Eminönü - Zeytinburnu Tram.
You get off Sultanahmet Station from Tram then you can reach to walk 1,2 minute to Hagia Sophia ( Ayasofya ).
You can reach from Eminönü or Beyazıt to walk.
İETT Public Buses - Which public buses to way Eminönü
İETT Public Buses - Which public buses to go Beyazıt

You can see lots of fish in the Basilica Cistern water. In my opinion, the Basilica Cistern is a wonderful place where must see.
Also It rarely has some events such as concert or theatre..
Basilica Cistern Events

Medusa
The two Medusa's head columns found in the northwest corner of the cistern are the great examples of the Roman Age art sculptures. It is not known exactly where these two heads came from, but there is rumour saying that they were brought here after being removed from an antique building of the late Roman period.
  The history of the mythological rumour of Meduca one can come acroos the following story: It is said that Medusa was one of the three underground Gorgona Giant sisters. Out of these three sisters only Medusa was mortal and she had the power of transforming people who looked at her into stones. It is said that in the old times.the statues and pictures of Medusa were placed in very important buildings and private places to keep them away from bad omens.
  In another rumour, Medusa is said to be a girl who was very much proud of her black eyes long hair and beatiful body. For a long time she was in love with Perseus, the son of Zeus. At the same time goddess Athene was in love with him and she became jealous of Medusa's love with Perseus. For that reason she turned Medusa's beautiful hair into horrible snakes. T Then whoever looked at Medusa turned into stone. When Perseus saw that Medusa was bewitched and she was turning people into stone by a mere glance, he cut her head, then won many wars by showing his beloved one's head to enemies. From that time onwards it is said that Byzantine swords handies were stylised with Medusa's head.