I'm trying to recreate a site, and one part of the content is supposed to show the distance relative to the user's location, like this:
Does anyone know of a way I can accomplish this?
You need to install the Geolocation Field module and the example submodule that comes with it.
In the examples you will find a view that made exactly what you need, and you only will need to clone and edit the view.
Geolocation Field provides a field type to store geographical locations as pairs of latitude and longitude (lan,lng). The Drupal 8 version also provides a views proximity search plugin. Geolocation Field can be used with all fieldable entities like nodes, users, comments, taxonomy terms, etc.