Aurora is a city in Center Township, Dearborn County, Indiana, United States. The population was 3,750 at the 2010 census. According to t…Aurora is a city in Center Township, Dearborn County, Indiana, United States. The population was 3,750 at the 2010 census. According to the 2010 census, Aurora has a total area of 3.087 square miles, of which 2.76 square miles is land and 0.327 square miles is water.