This is a write up for the reasons Yuu had decided to move to Inaba. Note, it is not complete as I need to work some details with Kazuki/Tohru's mun for some points!
After the events of P3, with the Dark Hour gone, Keita decided to confess his crimes. After substantial evidence was found, Keita was arrested for aggression (on Kazuki), and terrorism crimes for the Mall Bombing events. He was offered some kind of deal to reduce his sentence, however, he refused to make the names of everyone else who was involved in the Bombing and thus was not allowed it.
Although Yuu knew it was something necessary, as Keita had to pay for his mistakes, it was kind of hard for him to deal with it. The fact that his brother used to be a famous idol made it all the more difficult, as the case gained more popularity, and interviewers would keep bothering him around. Needing some sort of calm setting, but not wanting to go back home, Yuu decided to apply for the student exchange between Yasogami High school and Gekkoukan High school, successfully getting in.