Cincinnati, IndianaCincinnati, nicknamed Little Cincinnati, is an unincorporated area located in the Center Township of Greene County, Indiana, United States.HistoryA post office was established at Cincinnati in 1874, and remained in operation until it was discontinued in 1934. According to tradition, the community was named when a visitor told the innkeeper that the surrounding hills and whiskey made him recall his home in Cincinnati, Ohio.EducationCincinnati has a public library, the Eastern Branch of the Bloomfield-Eastern Greene County Public Library. Eastern Greene High School is also located in Cincinnati despite having a Bloomfield address.