In electrostatics, the field inside a conductor is zero. By electrostatics, I mean an isolated conductor. If it is placed in an external field, the free electrons in the conductor would be acted upon by the field and would more towards the surface closer to the positive end, leaving behind positive atoms (or I should say ions). This separation of charges produces a field that opposes the external field. The separation takes place until the two fields cancel each other out. At this point the electron would be pulled by the the positive ions with the same force as the external force is pulling it in the opposite direction.
A copper wire, it is not an isolated conductor. It is in a circuit. The free electrons would be pulled out of the wire by the current source. As in the previous case they are not forced to settle onto the surface of an isolated conductor. So in a copper wire, electrons flow in the interior region as well.