We can think the charges go to the outer surface of a conductor to minimize the electrostatic potential energy of the system. We can check this using a simple calculation using a charged sphere.
A uniformly charged sphere would have $20\,$% more energy than that of a very thin spherical shell with the same radius and the same charge as in the former case. As the potential energy would be less if we distribute charges uniformly over the surface rather than distributing the charges uniformly throughout, we can say, the conductor prefers having charges on the outer surface. Here's my question then:
Suppose I have a conducting sphere on which a charge $Q$ is to be distributed. Now, suppose I divide the charge into two equal parts, $Q/2$ each, and place them at two diametrically opposite ends of the sphere. Now the potential energy of the configuration becomes $75\,$% less than that for charges distributed uniformly over the surface. Then why doesn't the conductor prefer this kind of distribution which can minimize the potential energy further?