Balin's camp - running the gantlet
Edit: With recent changes to quests in Nud-Melek and Zelem-Melek, you don't even need to go here any longer.
Balin's Camp is located in Nud-Melek, midway along a corridor that runs between The Chamber of Mazarbul and The Deep Crossroad. Now, it looks accessible on the Durin's Way map that comes with the game but it isn't. The eastern end of the Chamber of Mazarbul is blocked off with rubble.
The blocked hallway from the east side of the passage.
To get there you need to get to the eastern end of Nud-Melek, near where the passage from The Fanged Pit joins. Then you need to run a gantlet through a variety of orcs and gredbyg to reach it, assuming they're of a level to attack you. Balin's Camp is midway, and there are two things there to click for quest updates.
Annotated Nud Melek map