The Fellowship encounters the Balrog in Moria, the underground realm in J.R.R. Tolkien’s Middle-earth.
Moria was originally called Khazad-dûm by the Dwarves. It became the greatest of their ancient cities and mines, extending beneath the Misty Mountains. The Dwarves awakened a Balrog while mining for mithril, and the creature drove them from the kingdom. Afterward, Moria became a dangerous abandoned ruin occupied by orcs and other creatures.
The Fellowship enters Moria after the mountain pass of Caradhras proves impassable. They pass through the abandoned city and discover the remains of Balin’s colony. In the Chamber of Mazarbul, they learn that the colony has been destroyed.
On the Bridge of Khazad-dûm, Gandalf confronts the Balrog and falls with it. Isengard is Saruman’s fortress, Mordor is Sauron’s land, and Angband is an earlier stronghold of Morgoth, so none is the Fellowship’s underground destination.