srds, we've stayed at that campground, too. Very nice especially if your site backs up to the cliff over the Frio.
j-man, there's a family run place downriver from Garner called Neal's Lodge. They have some tent sites right next to the river but floods have really altered the original sites. I think there's one screened in shelter, too. They are primitive but you can drive (very slowly!!!) to each. There are not many and finding a level spot might be a trick. There are showers and flushies close by. Nothng fancy but hey! It's on the Frio! That makes up for a multitude of things!! they do offer cabins, and RV sites across the street. They are home to one of the best swimming holes in Texas. They offer shuttles to get you upriver for tubin (which they rent). Neat place and very relaxed.
Here's the link:
http://www.nealslodges.com/index.htm
Tent sites are not mentioned but I've seen tents there. You'd have to call. Good luck and happy camping!