It should be a standard feature in the Shopify cart to enter a zip code for a quick shipping cost estimate.
Shopify is frequently reminding me how much my store is losing to abandoned carts. I presume a huge reason for this is that there isn't a quick user-friendly way for buyers to get a shipping cost estimate before checkout. Sure you can get one during checkout, but only after entering name and address and all that. Most buyers won't want to go through that hassle to get the shipping cost. When I'm shopping I hate sites that make me enter all that info first. I don't have the patience for that so I surely don't expect my customers to.
It seems the only option is some custom add-on, but I'm not a developer so that's not a user friendly work-around. This should be a standard feature for any ecommerce platform.