Want you want is to apply a default destination to a new quote, so that Magento thinks it will be shipped there and thus show shipping costs to that location. Luckily there's a small extension that does just that: http://www.rapidcommerce.eu/blog/2012/04/allways-show-shipping-costs-in-magento/ (note the updated version, it's still working on newer versions of Magento even though it was released in '12).

You can find the settings in the configuration under Shipping Settings.

What you want is to apply a default destination to a new quote, so that Magento thinks it will be shipped there and thus show shipping costs to that location. Luckily there's a small extension that does just that: http://www.rapidcommerce.eu/blog/2012/04/allways-show-shipping-costs-in-magento/ (note the updated version, it's still working on newer versions of Magento even though it was released in '12).

You can find the settings in the configuration under Shipping Settings.