Where would you have to be in either the northern or southern hemisphere for the Sun to remain below the horizon for a 24-hour period for at least part of a year?

You would have to be within the Arctic Circle in the northern hemisphere or within the Antarctic Circle in the Southern Hemisphere to experience a period when the Sun remains below the horizon for 24 hours or more. This phenomenon occurs due to the tilt of the Earth's axis, causing polar regions to have periods of continuous daylight or darkness during specific times of the year.