If you were to drive to some city south of your current location, how would the altitude of the celestial pole in the sky change?

For northern hemisphere, the altitude will decrease. For southern hemisphere, the altitude will increase

Explanation:

Because of the spherical shape of the Earth the altitude (separation from the horizon in degrees) of the celestial pole changes as per the latitude of the place. The altitude of the celestial pole is equal to the latitude of the observer.

If the observer is in the northern hemisphere and moves south the altitude of the celestial pole will decrease.

If the observer is in the southern hemisphere and moves south the altitude of the celestial pole will increase.