First set the mood:
All of the paved roads are very safe and easy to drive at night with the possible exception of the road up to the basin which has some sharp hairpin turns. On that road if the road sign says 5 mph you really need to slow down to that speed. We have camped numerous times at BBNP and I would agree with the places Texhills recommended. I guess you will be there near the full moon. A beautiful evening shot would be of the full moon coming up over the Sierra Del Carmen as the setting sun lights it up. I have seen photographers set up with tripods on the side of the road approaching Rio Grand Campground waiting for it.
Don't stay at the Rio Grande Village!! The only good thing there are paying showers.. Camp at the Chisos Basin, from there you can take day trips all over... BTW, if you climb all the way up to Emory, you will have a choice to scramble up a peak on your left, or one on your right, if you want to see the medallion, choose the one on your right. We chose the left and were too tuckered to scramble again knowing we had a lot more hiking in front of us