Columbia, Fayette County, IndianaColumbia is an unincorporated community in Columbia Township, Fayette County, Indiana.HistoryColumbia was laid out in 1832. It took its name from Columbia Township. A post office was established at Columbia in 1833, and remained in operation until it was discontinued in 1903.GeographyThere are only three roads in the entire Columbia area: South County Road, West Columbia Road and West Monroe Street.