A bathroom mirror serves as an integral part of most people's day-to-day routines. As such, it needs to be at a height that allows a person to fully view his face, hair and shoulders or upper torso.
Because the mirror is in the bathroom, the possibility exists for it to get continually splashed with water. It needs to be at least a foot or more above the sink, depending upon the size of the mirror and the height of the sink.
Not all family members stand at the same height. If children will be using the mirror to get ready for school, consider either hanging it low enough for them to use or bringing in a small stool upon which they can stand.