Not sure of the origin of 'go south', but it has a general meaning of to decline, to move in an undesirable direction, to deteriorate. I can only assume that it comes from the fact that if you look at the compass, north is generally considered 'up' and south is 'down'. As for 'go west'. This was an exhortation in America during the 1800 and possibly 1900s when 'the west' was largely undeveloped by European settlers and probably relates to the gold rush too. If someone 'went west' they had the opportunity to get land, make their fortune etc. I think both these terms are becoming anachronisms and not in common use anymore - at least I rarely hear them. Perhaps Americans still use them.