WHERE BETWEEN '2011-01-03' AND '2011-01-01'
potřebuje k porovnání název sloupce. Je to date sloupec?
Váš dotaz by pak měl vypadat takto:
SELECT *
FROM `stats`
WHERE `date` BETWEEN '2011-01-01' AND '2011-01-03'
AND `email`='[email protected]'
AND `city`='New York'
AND `location`='New York'
GROUP BY action