Burrill Lake Tourist Park, 8 Princess Ave S, Burrill Lake, NSW (south coast)
Ice cream truck far left, free rock climbing for the day, movie screen, playground to the right with shaded lego play area.
We stayed there in January 2014 and it was amazing! They have a playground set up for the kids next to the amenities block, a big tub of lego to play with, every night they played a free movie for the kids on a big outside screen, and they even hired a free rock climbing wall for the kids to have a go of one day. They let the ice cream vans in too. My kids were 6, 3, and 1 and they had a blast and made lots of friends.
In the nearby towns of Ulladulla and Mollymook there is Funland (a big arcade type place) and the rock pools for swimming and exploring. Check out Milton too for cute retro/vintage/antique shops and cafes (Pilgrims is vegetarian and does gluten-free).
We stayed early January (around the 6th), and paid $50 per night for 4 nights - powered site, 16ft caravan, peak, 2 adults, 3 children.