How to make a "player" or gameObject hover when idle?

if you want it to look natural you can always use a sine function to make it over on Y axis based on X time

http://jwilson.coe.uga.edu/EMAT6680Su07/Singer/Assignment%201/sine%20graph.html

and you could do something like this code where Y is your localPosition.Y and X = Time.DeltaTime

 float y normalHeight = something;
 void update()
 {
 if(state == state.Idle)
 {
     transform.localPosition = new Vector3(transform.localPosition.x, normalHeight + (theSineFormulaYouLike * Time.DeltaTime), transform.localPosition.y);
 }
 }