What you would do in this instance is create a custom form for your listings. In that form you can add or remove fields relevant to your listings so if you leave out state/province/country that is fine (although may have an effect on Google maps accuracy if you're using that).
The part of the custom fields screen which shows "state is a core field and can not be deleted", just means you cannot delete that from the list of custom fields - it's not referring to the custom form itself. Thanks.
