Hermione spent so much energy trying to get discharged from St. Mungos that when she was actually released, showered in a flurry of paperwork, she had no idea what to do next. There was nowhere for her to go. Her parents were in Australia. She had assumed, perhaps stupidly, that a member of the Order would be there when she was discharged, ready to whisk her off to some safehouse and tell her how brave she was, and to lie back and rest. 