Opening your hint path, you will be missed lead 
to think you will find the html table tags in side cart.phtml

.../template/checkout/cart.phtml

>> file content

<tbody><?php foreach($this->getItems() as $_item): ?>
    <?php echo $this->getItemHtml($_item) ?>
<?php endforeach ?>
</tbody>

Sorry! So to locate the file that is responsible for

populating your Magento cart, you will need to dig a little

deeper, at first this might seem confusing, but Magento has a 

perfectly good, "CONTROL N FLEXIBILITY". 

>> To start editing your cart, navigate to the directory below 

.../template/checkout/cart/item/default.phtml

All the expected html table tags (tfoot, thead, tr, td, table) 
controlling Magento's cart layout are all located under this file. 
Remember to first copy and paste this file inside your template
folder BEFORE EDITING it.

Happy theming.