Burnet Central Appraisal District is responsible for appraising all real and The district appraises property according to the Texas Property Tax Code and the. Get directions, maps, and traffic for Burnet, TX. Check flight prices and hotel availability for your visit. Burnet is a city in and the county seat of Burnet County, Texas, United States. The population was 5, at the census. Both the city and the county were. Barnet, Vermont TO Ellinger, Texas More. Barnet, Vermont TO Mexia, Texas More. The value of livestock dropped as well: Barnet, Vermont TO Dawson, Texas More. Barnet, Vermont TO Mount Enterprise, Texas More. Barnet, Vermont TO Collinsville, Texas More.