He died of old age in Spandau Prison, having been its sole inmate for the last years of his life. The prison was demolished to avoid it becoming a neo-Nazi shrine.
Hess did not die of old age. This fully referenced autopsy report: http://www.rudolf-hess.org/english/archiv/obdukt1_ e.php3?fs=8
states so unequivocally, concluding he died from hanging. Whether he hanged himself, or the scene was staged, is something I doubt we will ever know.