You know, that's a very good question. We know he got bit as a child, so he was probably living with his parents in a wizarding village somewhere, but after he graduated--he probably lived as a nomad. Moving from place to place, looking for work because as Rowling tells us, werewolves are hard-pressed to find good work because nobody wants to hire them. They are all afraid of werewolves. So Lupin probably moved around a lot.