We have always liked staying at Davis Mts State Park, but make a reservation because it's a pretty popular campground. they have elec, water and dump station.
Check out the McDonald's observatory website to see when the Star Parties are... try to aim for a moonless night or close to it.
Be sure to take in a night at the Marfa Lights rest stop about 7 miles or so east of Marfa. you can spend the night there. We've been twice and have seen the lights both times.