You're going to love Alpine and Big Bend. My buddy and I did a road trip from Houston to San Diego. We stopped in Alpine for dinner. Several shops and restaurants to spend a couple of hours wandering about. FYI, the town sort of closes down at night. We drove south to BB and did a loop drive. If we had the time, we would have spent a couple of full days there. Not sure about car rentals in Alpine, but I guess you can check that out.
Have fun.
dh