West Virginia. Alcohol Sales Hours (on-premises) : Beer/Wine served 7 a.m. - 2 a.m. Mon. - Sat., 1 p.m. - 2 a.m. Sun. Liquor served 8 a.m. - midnight Mon- Sat. Alcohol Sales Hours (off-premises): 7 a.m. - 3:30 a.m. Mon. - Fri., 8 a.m. - 3 a.m., Sat., 1 p.m. - 3 a.m. Sun. Grocery Store Sales: Beer, Wine and Liquor. Alcoholic Beverage Control State: No