Brewster County is a county located in the U.S. state of Texas. It is in West Texas and its county seat is Alpine. It is one of the nine counties that comprise the Trans-Pecos region, and borders Mexico. Brewster County is the largest county by area in the state - at 6,192 square miles it is over three times the size of the state of Delaware, and more than 500 squ…Brewster County is a county located in the U.S. state of Texas. It is in West Texas and its county seat is Alpine. It is one of the nine counties that comprise the Trans-Pecos region, and borders Mexico. Brewster County is the largest county by area in the state - at 6,192 square miles it is over three times the size of the state of Delaware, and more than 500 square miles bigger than Connecticut.