This appears to be Saigo Takamori often know as the last samurai - and has a film by that very name about him. He is most famous for his opposition against the Meiji government in the Battle of Shiroyama.
You can see here his very distinctive brow which is apparent in the scene in Chuunibyou too.
He has another statue in Ueno, Tokyo that has a dog beside him, which is probably what they are trying to replicate.
Kagoshima is his hometown, and there's a statue there in his likeness (without a dog):
