New York Rangers need their next head coach to have these five traits
Leadership
This is, by far, the most important trait that the next coach should have.
The Rangers are going to be loaded with youth in the near future, and the coach should be a shining example of what it means to be a pro. The coach should demand respect by the way he conducts himself on and off the ice.
The coach should also be somebody who can accept blame and criticism when it is deserved unlike his predecessor. Too many times Vigneault tried to deflect blame on to his players even when said player was not deserving of it at all. Instances like this one should not happen again.
They must be somebody who is a good communicator and that can be trusted by his players and he rest of his staff.
If the Rangers can find this in a candidate, then they are off to a good start.