It should go where you want the local pickup message to display.
you want it to show before the First name and last name, then change:
<p class="eC_OrderInfo"><?php echo((isset($_POST["shipping_firstname"]))?$_POST["shipping_firstname"]:"") ?> <?php echo((isset($_POST["shipping_lastname"]))?$_POST["shipping_lastname"]:"") ?><br />
to:
<p class="eC_OrderInfo"><?php if(isset($_POST['pickup']) && $_POST['pickup'] == "1") { ?>
Local Pickup
<?php } ?><?php echo((isset($_POST["shipping_firstname"]))?$_POST["shipping_firstname"]:"") ?> <?php echo((isset($_POST["shipping_lastname"]))?$_POST["shipping_lastname"]:"") ?><br />