Add date menu item to end of existing menu items (in primary location).

functions.php

<?php

add_filter( 'wp_nav_menu_items', 'gmj_add_date_menu_item', 10, 2 );
/**
 * Add date menu item to end of existing menu items.
 * 
 * @author Gary Jones
 * 
 * @param string    $items Menu items already converted to a string of markup.
 * @args  stdClass  $args  Menu arguments.
 * 
 * @return string Amended markup.
 */
function gmj_add_date_menu_item( $items, stdClass $args ) {
	// Limit to a certain menu location
	if ( 'primary' != $args->theme_location ) {
		return $items;
	}
	// Straight concatenation here. Could prepend, or do a regex replace to
	// insert the menu item elsewhere
	$items .= '<li class="menu-item right">' . date_i18n( get_option( 'date_format' ) ) . '</li>';
	
	return $items;
}