In those days, priests didn't always have a set parish. They went where they were needed, and Fr. Badin managed to range all over the landscape, from Pittsburgh to Illinois. His primary field was Kentucky, however.
In the 1830's, Fr. Badin was headquartered in the Cincinnati Diocese, and went to whatever part of Ohio needed him most. From 1835 to 1837, he helped out in Fremont and Tiffin, in what's now the Diocese of Toledo.
Fr. Badin retired ( At least as far as was possible ) to Cincinnati and died there, in 1853. HERE'S a brief account of his life.