Add Navigation Extras in Genesis

One can add additional content including search form, widget area after or in navigation menu in any theme based on Genesis Framework.

Here is the basic snippet to start with. Use this in functions.php

<?php
//* Do NOT include the opening php tag shown above. Copy the code shown below.

add_filter( 'wp_nav_menu_items', 'theme_menu_extras', 10, 2 );
/**
 * Filter menu items, appending either a search form or today's date.
 *
 * @param string   $menu HTML string of list items.
 * @param stdClass $args Menu arguments.
 *
 * @return string Amended HTML string of list items.
 */
function theme_menu_extras( $menu, $args ) {
	//* Change 'primary' to 'secondary' to add extras to the secondary navigation menu
	if ( 'primary' !== $args->theme_location )
		return $menu;
	//* Uncomment this block to add a search form to the navigation menu
	/*
	ob_start();
	get_search_form();
	$search = ob_get_clean();
	$menu  .= '<li class="right search">' . $search . '</li>';
	*/
	//* Uncomment this block to add the date to the navigation menu
	/*
	$menu .= '<li class="right date">' . date_i18n( get_option( 'date_format' ) ) . '</li>';
	*/
	return $menu;
}

Additional modification and CSS is required based on what you want to achieve.