The term can vary based on the region - 'down south' in the UK may refer to different areas than in the US. In the UK, he moved down south to enjoy Brighton's coast.
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General Direction
'Down south' often means moving towards a general southern direction, not a specific location. Let's drive down south until we find a good camping spot.
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Metaphorical Use
Sometimes used metaphorically for going to a place that's calmer or warmer. I'm tired of the city's rush, thinking of going down south.