mysqld - cannot connect to socket after changing datadir location
The problem is the mysql client program configuration.  You can specify the --socket=/NEW_DIR/mysql/mysql.sock command-line option or add it under the [mysql] section of your my.cnf file.

Please look at the documentation for specifying options through option files: http://dev.mysql.com/doc/refman/5.0/en/option-files.html

Since changing the socket path affects all the client programs, then it will make sense to update the global my.cnf and set the socket option under the [client] section.