How can I practice mindfulness meditation with sound, not breathing?
Sound is a valid object of mindfulness, one of the six sense objects, part of the fourth foundation of mindfulness:


  "He understands the ear, he understands sounds and he understands the fetter that arises dependent on both; and he also understands how there comes to be the arising of the unarisen fetter, and how there comes to be the abandoning of the arisen fetter, and how there comes to be the future non-arising of the abandoned fetter." (MN 10, Bodhi trans.)


The point here is to observe sounds as something that gives rise to potential fetters (liking, disliking, conceit, possessiveness, etc.). Through mindfulness, one understands sound as merely sound, as impermanent, unsatisfying, non-self, and one relinquishes craving in regards to sound.

In my tradition, we remind ourselves "hearing, hearing..." as a means of cultivating mindfulness.