The Sith Academy on Korriban was a facility in use during the Jedi Civil War, dedicated to training Force sensitives in the ways of the Sith, and running archaeological projects in the Valley of the Dark Lords. However it was also used during the Legacy Era to train Force-Sensitives, in the ways of the Sith.
A Crystal Cave contained multiple, normally different colored Crystals used for Lightsabers, and jewelry. Most Jedi and Sith used Crystal Caves to retreieve the Crystals they desire, in order to make the beam, and determine what color the beam will be for their Lightsabers.