Coming into Austin from the east, take hwy 71. Then it's a straight shot to hwy290 west. After Fredricksburg, I'd head south to hwy 90 toward Langtry, Marfa, and Alpine. Then BBNP. Langtry has a boondock at the Judge Roy Bean museum. Marfa has the Marfa Yacht Club, an Airstream only CG, and Alpine has Sul Ross State U. When you get to El Paso, take hwy 375 north over the Franklin Mtns. Great views, no downtown on Transmountain hwy.
Two years ago, we tried Death Valley in early May. Heat was already over 100. Only campground with electricity was closed.