Minori Garden is an orphanage, most likely in Nagano. The orphanage is run by nuns.
Ganta Igarashi was sent here after Deadman Wonderland was shut down and he was acquitted by the court. Why he was sent to an orphanage is unclear, because it is said in the first chapter that Ganta was living with his father, meaning his father is still alive and that he is not an orphan.
After Karako visited Ganta and invited him to the DW Task Force, Ganta then left the orphanage.