How much farther away from a current-carrying wire would you have to stand in order for the magnetic field generated by the

wire to be half as strong?

Your question is open ended therefore i will provide a general answer based on the general concept of  your question.

Answer : At half distance between the center of the Magnetic field the magnetic pole the effect of the magnetic field generated will be half as strong

Explanation:

Magnetic force  ∝  1 / d^2

This simply means increase in the squared distance of an object leads to the decrease in the effect of the magnetic field generated by a current carrying wire.  

Hence ;  

At half distance between the center of the Magnetic field the magnetic pole, the effect of the magnetic field generated will be half as strong