Add message to WooCommerce email if shipping method is local pickup.

functions.php

<?php

add_action( 'woocommerce_email_before_order_table', 'add_order_email_instructions', 10, 2 );

function add_order_email_instructions( $order, $sent_to_admin ) {

	$shipping_method = @array_shift( $order->get_shipping_methods() );
	$shipping_method_id = $shipping_method['method_id'];

	if ( ! $sent_to_admin ) {
		if ( 'local_pickup:5' == $shipping_method_id ) {
			// local pickup option
			echo '<p><strong>Instructions:</strong> Please contact us at 000-000-000 to arrange a pick-up time.</p>';
		} else {
			// other methods
			echo '';
		}
	}
}

?>