How to display custom post meta in the appearance->menus page

The menu items boxes are created by the class Walker_Nav_Menu_Edit in wp-admin/includes/nav-menu.php.

Thus to alter those boxes you’ll have to make your custom Walker I guess.

But if you mean adding the new value to the nav menu meta-boxes (the boxes to the left side of the page) this will do the job:

The function that adds new meta_boxes:

function my_function() {
   add_meta_box( 'foo', __( 'Fooo' ), 'callback_function' , 'nav-menus', 'side', 'default' );
}

The callback that renders the output for the new boxes:

function callback_function( ) {
  global $wp_meta_boxes;
  var_dump($wp_meta_boxes);
}

And you can use both:

add_filter( 'manage_nav-menus_columns', 'my_function');

or

add_action('admin_init', 'my_function');