Go in March. It gets hot there early.
On the way there or home checkout Fort Davis Mtns State Park. We usually stay at Balmoreha State Park which is 40-miles north of Ft Davis. But we prefer Ft Davis SP overall.
Lots of miles between places out there. Heck, it's something like 80 miles just to drive into the National Park. Marfa, Alpine and Marathon are worth a visit but far between each one. Of course, Terlingua is nearby, quirky and interesting. And the State has a Big Bend Ranch State Park that is supposed to be worth checking out.
And some rich California land developer is trying to create a super swanky golf resort next door called LaJitas
. I haven't been there for nearly 10-yrs, so I don't know if he's succeeded yet or not.