Board Thread:Questions and Answers/@comment-24989822-20140608121309/@comment-679780-20140731141436

It never states exactly whetre it is. I believe it is in the South Pacific since it is the south. However I do also believe it is close to the mainland as the map of Sonic Adventure 2 Battle depicts a small green island of various hexagons near Route 280 where Green Hill Zone can be later accessed So if Sonic Adventure 2 takes place somewhere in North Atlantic Ocean then perhaps South Island is called South Island because it's south of Capital City off the coast.

I like to believe that small green island is South Island itself only stylised to be smaller or just there for the conveniance of Green Hill Zone.