Despite what it proclaims on its website, I would hesitate to say that Augusta is in the wine country of Missouri. The real wine country is near Hermann, which is about 40 miles away from Augusta. Augusta is very small and has practically zero amenities for camping. The closest camping that would be worth going to is Pin Oak Creek which is about 20 miles from Augusta.
Welcome to Pin Oak Creek RV Park
Hermann has a city park with campsites. The DW and I just stayed there a few weeks ago. Make sure you get a full hookup site. The electric only sites can be in a parking lot far from the shower house. I recommend full hookup site 7, 8 or 9.