You have 2 options of changing this url (actually there are more but 2 of them are easier).
The first one, if you want always a specific url you can use the layout file inside the cart block definition this:
<action method="setContinueShoppingUrl"><url>Some/url</url></action>
But this can result into issues. It is better to create your own helper that has a method getContinueUrl that returns the desired url and modify the markup above to
<action method="setContinueShoppingUrl"><url helper="helper_alias/getContinueUrl" /></action>
Or you can create an observer that set's the url on the block:
Mage::app()->getLayout()->getBlock('checkout.cart')->setContinueShoppingUrl('URL HERE');
The second option is to create an observer that sets the url in session. This can be used if you want a dynamic continue url. Add this in your observer.
Mage::getSingleton('checkout/session')->setContinueShoppingUrl('URL HERE')
There is always the 3rd option of rewriting the cart block but there is no need for that when you have the 2 options above.
And as far as Where should this button link to? I think this is opinion based. It can link to the last visited category, to the homepage, to one of the crosssels products of the last product added to cart, to the advanced search.