In New York State how old does a minor have to be to decide were they want to live?

Want doesn't really enter into it. Are you asking about choosing between your mom and dad?

The courts decide. Your opinion will be heard, and considered, but you don't get to "choose". There's a reason why the choice was made to begin with.

Legal age in New York Stae to move out of your parents home

18. A child (minor) cannot choose. The non custodial parent needs to file in court for a modification of the custody order. Depending on the age of the child their preference will be listened to and given weight, but the ultimate decision is in the hands of the court.

There is no age that a minor can decide. At 18 they may move out. In a custody hearing, between parents, children about 12 to 14 and older, may be allowed to testify as to what they would like. But the judge will listen to all evidence and what the child wants is not the major factor he looks at.