The last time we were in Chama, several folks were camping at Heron Lake State Park. Yes, it's an 18 or 20 miles drive to Chama.
At $14 for a W/E site - the drive might be better than the price at Rio Chama. Or if you need a FHU site - $18 at El Vado Lake SP and a 30 mile drive might be worth it.
Personally I prefer Rio Chama. The only thing I don't like about them is that their rates are not on their web site, but RV Park Reviews will give you an idea what they charge.