As of current lore and locations, it is implied that all forms of higher education in magic are handled by the arcanist, thaumaturge and conjurer guilds. There is no such a thing as an academy, though we dont know about Ishgard and the other city state that was not in the last Beta.
Garleands probably have academies, though, but they will be probably be focused on magitek and engineering, as most garleans are incapable of magic.
Garleands probably have academies, though, but they will be probably be focused on magitek and engineering, as most garleans are incapable of magic.