Big Bend NP can be a spectacular visit, especially when it rains in the mountains. Not often, but a spectacular view, sometimes you can see the rain evaporating before it hits the ground. Unless you like heat, or have real good AC in your rig, stay away in the summer. When I was young, our scout summer camp, in Fort Davis, averaged in the 110's during the day, more like Arizona than anywhere else. Know know the old saying; but it's a dry heat! <rolling laugh> Plenty of rattlesnakes, and oh yes, there are mountain lion's. You can hear their unique sounding cries at night. There's the "Ghost Lights" in the hills and mountains near Marfa. There was once a huge scientific telescope near Fort Davis, don't know if it is still there, and there is the old restored fort itself. There is Alpine, a unique town, along with valleys and spring fed creeks in the middle of a desert like hill and mountain environment.
If your very brave, and have a wild side, there is the Terlingua chili cookoff in the first weekend in November. It's the "Superbowl" of all of the chili cookoffs in the Nation. They actually have it on a ranch 50 or so mile from Alpine near a tiny "one horse" town named Study Butte, TX if I remember my directions correctly. There is no such thing as a town named Terlingua. Be forewarned that the event is more like a motorcycle rally, or a Texas "Woodstock", than a formal cooking contest. I was very young last time I went.
On a last note, be careful, you are very close to the border and there are a few serious outlaws wandering in the wilderness in that area. Most are illegals that have crossed the border. It has always been that way since the days of range cattle, no fences, and cattle rustling before Texas was a state, and now days, probably worse due to the drug smugglers. We once had a good friend that was a border patrol agent in that area, he passed on due to illness quite a few years ago. It's perfectly OK to "sight see" but don't linger too long in any one area, especially if you are in a really nice rig, just keep moving. Be careful of strangers that can't speak english. If there is a well protected RV park available, you will be OK. Since I have yet to RV cruise this area, I don;t know the campgrounds. We grew up traveling that area almost every month as my father was a competition marksman and most of the competition events were in Marfa or Presidio. I do look forward to returning and making an RV cruise through the Big Bend area and mountains around Marfa, Presidio, and Alpine someday.