The Rim essentially includes all the outer planets (and their moons) in the Solar System past Mars. This includes Jupiter, Saturn, Uranus, and Neptune (and all of their respective moons). In theory, The Rim includes dwarf planets, but it is unknown whether or not they have been settled in the Red Rising Trilogy.
The Rim has had a rocky relationship with the rest of Society since its founding, thus reflected in the two Moon Lord Rebellions pushing for Rim independence. These rebellions were spurred on by a lack of Rim representation on Luna and trade sanctions remaining from the First Moon Lord Rebellion, among other things.