Hi, I think Morgan is not quite correct.

You have to list an address but you can choose if you make it public.
I had a client who works in a sensitive (security) area. They listed the business, kept the address private and were able to list themselves as a region.
Here’s how.

1 – Change your business name to add the word “Auckland” after the name [won’t help SEO but readers can see your intent]
2 – Go to the left sidebar “info” and select Service Area. Change this to “Auckland?” or “Auckland CBD” or whatever suits you. This will ensure it displays to people searching in that geography.
google business service area - Auckland
3 – make address secret [especially if you have a residential address and don’t want the public knowing this].

Get in touch if you need more help.