Did you put $meta_query into your $args array? Like this:
if ($_POST['plaats'] != '') {
$meta_query = array(
'relation' => 'OR',
array(
'key' => 'city',
'value' => $_POST['plaats'],
'compare' => 'LIKE'
),
array(
'key' => 'city2',
'value' => $_POST['plaats'],
'compare' => 'LIKE'
)
);
}
$args['meta_query'] = $meta_query;
query_posts($args);