Bearing in mind that I'm not experienced in Android so if this doesn't apply ignore me.
With the web version, the easiest way to achieve what you're looking for is to use the drawing API to create a circle of the radius you're looking for (in this case a mile) centered on your users location. You can then use the built in methods to find the corner bounds points of this object (unfortunately rectangular) to give you the long/lats you're looking for.