MySQL CONCAT address into string seperated by comma

CONCAT_WS() does not skip empty strings. However, it does skip any NULL values after the separator argument.

NULLIF(expr1,expr2) Returns NULL if expr1 = expr2 is true, otherwise returns expr1.
SO your query could be:

SELECT 
  CONCAT_WS(', ', 
       NULLIF(location_address1, ''),
       NULLIF(location_address2, ''),
       NULLIF(location_town, ''), 
       NULLIF(location_region, ''), 
       NULLIF(location_postcode, ''), 
       NULLIF(country_name, '')
  ) AS address
FROM
   countries c      
WHERE
   c.country_id = locations.country_id LIMIT 1