How far away from a wing's surface does the air stream remain unaffected?
A precise answer would be: Only outside of the supersonic shock cone. In subsonic flow the change has unlimited range, but dies down with the inverse of the distance.

A mathematical description is possible with the Biot-Savart law. It was first formulated for calculating the magnetic field induced by a current, but can equally well be applied to aerodynamics.

Now it depends on how much error you still accept. If you need the interference-free distance between two biplane wings, express that distance in multiples of the wingspan - that is how it scales. A few wingspans of vertical separation should be enough to make the interference between wings negligible. In flow direction the distance must be much larger: Munk's displacement law postulates that in inviscid aerodynamics the distance in flow direction between two wings makes no difference. In reality, air traffic control requires a separation of up to 8 nautical miles between heavy airplanes for the turbulence to die down or be washed away by wind.