This code generates some SQL which can achieve this on every table and column in the database:
SELECT
'UPDATE ['+T.TABLE_SCHEMA+'].[' + T.TABLE_NAME + '] SET [' + COLUMN_NAME + '] = NULL
WHERE [' + COLUMN_NAME + '] = '''''
FROM
INFORMATION_SCHEMA.columns C
INNER JOIN
INFORMATION_SCHEMA.TABLES T ON C.TABLE_NAME=T.TABLE_NAME AND C.TABLE_SCHEMA=T.TABLE_SCHEMA
WHERE
DATA_TYPE IN ('char','nchar','varchar','nvarchar')
AND C.IS_NULLABLE='YES'
AND T.TABLE_TYPE='BASE TABLE'