How do I exclude posts by custom field value?

You can use meta query in wp query to get required posts

  $args = array(
   'meta_query' => array(
     'relation' => 'OR',
      array(
        'key' => 'city',
        'value' => 'Melbourne',
        'compare' => 'NOT LIKE'
      ),
      array(
        'key' => 'city',
        'value' => 'Melbourne',
        'compare' => 'NOT EXISTS'
      )
   )
  );
  $query = new WP_Query( $args );