You shouldn’t edit the WP Core because it will break at the next update. I believe the easiest way is to use jQuery. Use a filter to add the jQuery code to the page.
function cystom_jquery_code() {
echo '<script>
jQuery("body").after("div class="myClass"></div>");
jQuery("#wpwrap").before("<div class="beforeClass"></div>");
</script>';
}
add_action('admin_head', 'cystom_jquery_code');