Try this:
$sql = "SELECT * FROM myTable WHERE cityname LIKE '%New York%'";
$query = mysql_query($sql);
The word which will be searched should be in single quotes. Only the word will be a table field / column.
You should use PDO (More information about PDO) for this, not the old and deprecated mysql_* functions. See comments above from Mark Baker and Elias Van Ootegem.
//comment #1:
use var_dump($query);
for debugging.
Successfully connect to the mysql-server?
Use http://de2.php.net/manual/en/function.mysql-errno.php or http://de2.php.net/manual/en/function.mysql-error.php to get errors.
//comment #2:
what do you get with echo mysql_errno();
and echo mysql_error();
//comment #3:
It seems the user need a password or has no access or permissions to the selected database. Check your connection settings on mysql_connect($server, $username, $password)
or the permissions of the user with phpMyAdmin.
//comment #4:
//comment #5:
Which output you get with SHOW GRANTS FOR my@localhost
on phpmyadmin.