Adding geographical information on a registration page

I'm trying to get my head around developing a delivery app for restaurants where I make a a WP site with WooCommerce and a local payment gateway. I need the app to only allow registrations from addresses a certain distance, in accordance with how far the store wants to do deliveries.

I'm pretty sure you can integrate Google Maps API into the registration forms, I'm just not quite sure how to do it.

EDIT:

As comments have noted it probably would be easier to hardcode postcodes that the shop is willing to deliver to than actual geocoding