We spend about 10 days every summer at a NFS campground about 30 miles from Chama toward Antonito, CO. I've been going to this campground since I was a young lad, my kids grew up going and now our kids and grandkids also go with us. The area is nice and seldom crowded. If you don't mind dry camping I would recommend this campground. It's right on the Conejos River.
A few things to see that are reasonably close are:
Cumbres Toltec Railroad: Runs from Chama to Antonito over La Manga and Cumbres Passes.
The Great Sand Dunes: About 20 miles east of Alamosa toward Walsenburg. Truly an amazing place.
Pagosa Springs / Durango, Silverton, Ouray are great areas to visit. Beware that currently, you can't go to Pagosa Springs via South Fork and Wolf Creek pass due to a fire. The road is closed and the Wolf Creek area is being evacuated.
A trip to Mesa Verde would be great as well to see the cliff dwellings.
You can drive up to Lake Platoro which is pretty scenic, but it's 25 miles of gravel road.
There's not a lot to do in Chama proper other than knock around the train station but it is a very pretty little town right on the Rio Chama.
