The Central Coast might work for you. Public transport is a bit iffy but you could try. By half an hour from Sydney, do you mean the city, or another part of the city? What were you hoping to visit?

Because 30 mins from the city is still within Sydney and just as busy. Lol

Or try the northern beaches - I know some friends have stayed at a great caravan park there and raved about it. Has great kids facilities apparently.