". . . travelers should be at their observation location a minimum of a couple hours before totality. The role of State and local DOTs may include instituting roadblocks or other measures to keep people from making illegal turns as they drive around looking for "the perfect spot" as eclipse totality nears." (see FHWA's Transportation Fact Sheet for State and Local Departments of Transportation for more details)
See also FHWA's page on the eclipse for additional tips and for detailed travel information by state.