I've been to Big Bend 4 times now, during the xmas vacation too, it's the best time of the year to go, perfect weather. I think the RV is in the chisos basin, correct? We always did primitive camping. Anyways, I highly recommend doing the south rim trail. Walking up to the edge from 30 feet away then arriving at the edge, it looks unreal. From there you can follow the rim left or right, back to the basin. Awesome views in either direction, but I personally like the right (west?) trail.
Also, hike up to Emory Peak. You will pass it on the way to the South Rim, but don't try to do both trails in one day, Emory Peak is quite exhausting. Also the Window Trail is a nice one too. I will upload some pics in a bit....
Looking into Mexico from the South Rim:
Emory Peak, looking south:
Emory Peak, looking at the basin:
Javelina on the Window Trail: