Where does a rotation go when I Apply it to a mesh? When you Apply a rotation to a mesh, where does it go, and where can you find it in bpy? 

I.e. bpy.data.objects['mesh']. ...?
The transformation is applied directly to the world space locations of the vertices/edges/faces, then removed from the object transform. As a result, it is lost, as it is no longer distinguishable from any other change to the base mesh data. Such as edit mode changes, other applied transforms, applied modifiers, or the original script/primitive/tool that spawned geo there in the first place.