There are several scenic routes through the Hill Country going from Austin to Big Bend, but fastest is to take US 290 west through Fredericksburg and Harper, which intersects with I-10 just east of Junction.
Merge with I-10 west to Fort Stockton. Total mileage Austin to Fort Stockton is about 340. From Fort Stockton, you can go south on US 385 to Marathon, 58 mi. then continue south on US385 to Big Bend National Park From Fort Stockton, you can also continue on I-10 west for 9 mi., then turn south (left) on US 67 to Alpine, another 58 mi. This is a more roundabout way to get to the Park, but closer to Terlingua, Lajitas, Ross Maxwell Scenic Drive and El Camino del Rio. Enter Alpine, right after you pass Sul Ross State University, the road divides. Go about two blocks take a left on TX 118. Go 78 miles to Terlingua/Study Butte Junction. Take a right on TX 170 for Terlingua, Lajitas and Big Bend Ranch State Park. Keep going on TX 118 3 mi. for Big Bend National Park entrance.
By taking different routes to and from Big Bend, you can see lots of Texas.