This Carmelite convent, 6km southwest of Heiligenkreuz, was the site of the famous Mayerling murder-suicide of Emperor Franz Joseph I and Empress Elisabeth's son Rudolf and his young lover, Baroness Mary Vetsera. It's something of a macabre curiosity for Austrians (the scandal continued long after the monarchy itself was no more), but the convent post-dates the event and there's nothing to actually see that relates to it.
Rather creepily, the altar in the chapel was built exactly where the bodies of Archduke Rudolf and Maria were found.