Sadly, as you've found out, there are few commercial RV parks in the greater Augusta area, and the ones that are there leave a lot to be desired.
As Recks noted above, there are quite a few COE and SP campgrounds up around Clark's Hill Lake (they only call it Lake Thurmond on the South Carolina side :) ) Some of the nicer ones are Petersburg and Ridge Road on the Georgia side and Modoc on the SC side of the lake. All of these are 45 minutes to an hour from North Augusta.
If you are active or retired military, or 100% DAV, there is also a really nice military campground on the lake. It's called Pointes West Army Resort.
Have a safe trip!