Gloombound Mine is an Orcish mine located south-east of Windhelm and north of Mzulft. It is adjacent the Orc stronghold of Narzulbur. To reach the mine, enter the stronghold, then cross the bridge and continue straight along the path.
The Orcs remain rather unfriendly until the Dragonborn has completed the quest The Forgemaster's Fingers.
Note that some of the cave floor and walls are unstable and can collapse. This mine is a significant source of Ebony Ore.