Act 2: Rise To Power
During Act 2, Minas Morgul appears in two missions, The Tower of Sorcery and Army of the Dead, Apart from that, there is no reason to go there as the orcs are of a very high level in the region.
Act 3: Shadow and Flame
After taking Isildur's ring of power, Talion and an army of Revenants storm the city banishing Nazgul in the process. After a pretty hard boss fight against the Witch King of Angmar, The city becomes the home and fortress of Talion.
Act 4: The Shadow Wars
During the Shadow Wars, Minas Morgul served as Talion's fortress and home until his eventual fall, upon which the city once again fell into possession of The Witch King.