Just to add to the conversation - I drove through Whites City this afternoon and can confirm that it is pretty simple and not much in the way of amenities. I also drove through Carlsbad Campground RV park and found it better but the newer open sites were still close together and just open gravel.
FYI - right now many of the parks in this area are full of pipeline construction folks who are staying for some time on various jobs so availability in some parks is tight.
For a night or two - there is a very small park right at the East end of the Hwy 62/180 bridge over the river . Have not stayed there but have driven by it many times and it looks pretty nice and is right on the river. It is the Pecos River RV Park and has only 12-15 spaces (I think) and this afternoon was about half full. I did see a sign that the property is for sale but do not know if that will impact staying there or not.
Anyway, just some current observations. As most have suggested the KOA or the state parks might be a better choice. There is also Guadalupe Mtns NP down the road which has a small, no hookups RV area if that might work for you.
Hard to say what would work best in Nov. Pay attention to the weather forecast and have a good time.
Terry