This thread is their to support plugin 'Postcode Auto Fill':
https://www.zen-cart.com/downloads.php?do=file&id=2370
When you enter postal or zip code in a form, this plugin auto-fill state, city and, if data available, street address fields in 'create account' page, 'address book' edit and 'new address checkout' pages.
If multiple choices are available a nice Jquery/Javascript popup tool will appear on the right when hovering the field.
Thanks to an AJAX query, all this is done on the fly without need to reload the form.
Postal/zip code data are stored in database in new tables (One for each country). Three countries data are provided, US, France and Japan. Of no need to install all of them, you need the ones where most of your customers are at minimum.
This plugin is nearly drop in type and should be easy to install. Hard part might be to build your own data for your country if not available yet. Basic instructions to do so are on the read me file and if it is not enough you have this thread.