I use the following wordpress theme ([url removed, login to view]). I currently have it set up so the ability to make listings and see the full details of a listing are behind a paywall.
I want someone to create an option when a user signs up to receive notifications when someone signs up within 5-10 miles of them. This can simply be 2 check boxes on the form in which they create a listing (one stating "send me an email when someone signs up within 5 miles of me," the other, "send me an email when someone signs up within 10 miles of me." The boxes should be mutually exclusive so they can't check both but only one (so they don't receive 2 emails each time someone signs up < 5 miles away).
You will also need to add the functionality for them to receive these automated email notifications.
Notably, the theme does have geolocation in it which I presume would make this easier. Also, it already sends some automated emails when users register (computer generated password with a link etc).
Also, these changes you create should remain stable when when the theme and other plugins are updated. If this requires using a "child" theme, the website already has one that you will need to add to.