I've stayed at the Lightner Creek Campground twice a few miles west of town. I only got a cabin for the night each time since I was passing through on the motorcycle. It is a nice place, has a creek running right through the middle of it. There are on-site bathrooms/showers. Was quiet both times I was there.
The CG isn't too far away from Durango, and entering town will put you right where you need to be for the train ride.
If I ever end up there with my trailer, I would not hesitate to stay at Lightner Creek with my trailer.