There used to be a KOA campground on the main road east of Durango, which I stayed in during 1968 and 1971. Have no idea if its still there, but the place Russ mentioned along the D&S sounds like a great location. If you miss a train, at least you hear it and can watch it go by!!
There is the campground right in Chama, along the tracks near the Rio Chama bridge, which is where I suspect most stay.
Back in 1968 we stayed at a small campground called Aspen Glade, which is along the Conejos River on the main road to Chama, before you make the big climb. There were no facilities there except for restrooms, but it was really nice by the river with our truck camper back then. You could probably google campgrounds near whatever place you want and get some other suggestions, along with images on various websites. We were in college during our 1971 trip and we camped most of the nights on that trip in tents. I spent a total of $100.00 on a two-week trip that year. Gas wars in Kansas for 19 cents helped a lot, plus splitting stuff with 3 other guys including a U-haul for two motorcycles and our tents and other stuff. It was a fun trip and good way for us to save up for a bigger trip for steam to Europe in 1972!!
Greg Scholl