Appleby is a city in Nacogdoches County, in the U.S. state of Texas. The population was 552 at the 2020 census. According to the United Stat…Appleby is a city in Nacogdoches County, in the U.S. state of Texas. The population was 552 at the 2020 census. According to the United States Census Bureau, the city has a total area of 2.1 square miles, all land.