Round Valley is a census-designated place in Apache County, Arizona, United States. The population was 487 at the 2010 census. The CDP is located in northern Gila County, just south of the town of Payson. Arizona State Route 87, the Beeline Highway, forms the western edge of the CDP and runs north 3 miles to the center of Payson. According to the Unit…Round Valley is a census-designated place in Apache County, Arizona, United States. The population was 487 at the 2010 census. The CDP is located in northern Gila County, just south of the town of Payson. Arizona State Route 87, the Beeline Highway, forms the western edge of the CDP and runs north 3 miles to the center of Payson. According to the United States Census Bureau, the Round Valley CDP has a total area of 4.8 square miles, all land.