Hello,
When Tweeting from your phone with exact GPS coordinates, you can indeed retrieve the location information from coordinates, with the inner coordinates array formatted as geoJSON (longitude first, latitude second), and a type with value Point.
When submitting an approximate location like a city or a neighborhood from your computer, you should look into the place nested object. Your can find here a Polygon as a type, an array of coordinates describing a bounding box for this location as well as its name, type, country, and more.
Check out the object documentation for [node:7286] to find more information.