From a conversation I had with Esri a few days ago about this issue....
Please confirm that the locator widget works on your mobile browsers over https. You can use the following web app, in case you do not have SSL enabled on your server: http://arcg.is/2crOHOA.
On your device with iOS 10, are you using Chrome or Safari? Make sure you enable location services under Settings > Privacy > Location Services > Chrome/Safari (Set to While Using).
I can confirm on iOS 10.0.1 the location widget works on both Chrome and Safari.