Keep in mind that at Cottonwood generators are not allowed. If you can do without them, that would make a very nice 'second place'. It's a beautiful campground.
Rio Grande Village campground (not the RV park) is also very pleasant.
We've been to the park quite a few times and sometimes we stay in one campground; other times we've moved between the two. We had solar panels so didn't need the generator.
From San Antonio you'd be coming in on Hwy 90. You'll take 385 to Panther Junction and then make your choice of campgrounds.
Study the park map and see if one or two campgrounds would work for you. They are both about equal distance to Panther Junction. There's lots of hiking around the Panther Junction area and I'd say less at Rio Grande Village.
You might want to go to Cottonwood first and stay until you think your battery power would be low and see the sites and some hiking around there, including a trip to Terlingua and hikes in Chisos Basin. Then move to Rio Grande Village and recharge your batteries during the move. You can also use generators at Rio Grande to charge back up. Here's the park map:
https://www.nps.gov/bibe/planyourvisit/maps.htm