The Dark Cave is a cave found lining Route 45 and Route 46, which can be found going down from Blackthorn City.
There is not much to do in this cave other than catching for the Pokédex or to mine gemstones.
Here is a list of the gemstones found in this cave. Here is a list of Pokémon found in the Dark Cave.
Here is a screenshot of the entire cave. (ignore the dim thing in the middle, its a cave, makes it automatically dark.)