There are plenty of places to decide for down this way. There are camping sites all along the Clyde river which runs west from Batemans Bay. You can access these by heading out to Nelligen and turning off onto River Road. This takes you out to Shallow Crossing, and if you keep going you will end up out the back of Ulladulla/Milton and it may even go all the way up to Nowra. There are also numerous caravan parks to choose from at Batemans Bay or Nelligen.
South of Batemans Bay you have Mogo. Anywhere west of the highway is gold bearing but you will not have any designated camping areas or rivers.
South of Mogo you have Moruya. There are a few camping areas to choose from depending what you want to do. There are a few caravan parks available. There is also North Head primitive camp ground near Moruya airport. Great spot to set up base. Within 10 minutes from Mogo. It is also only under an hours drive to most of the other prime gold bearing soil in the south coast area, ie; Nerrigundah,
You can keep heading south to Bodalla (gateway to Nerrigundah) or to Narooma, depending on what tickles your fancy.
Hope this helps. Need any other info let me know.