Mataranka Hot Springs has always been my favourite family camping spot. It is a very popular watering hole, so It's best to get there early for your long weekend or if you are lucky enough to camp when it is a quite period of the year (not during school holidays).
I really enjoy the warmth of the crystal clear natural hot springs, as it is quite refreshing after the relatively short drive from Darwin. It takes about three and a half hours by road and is very achievable with small children in the car. The flow of water is slow, which makes it very safe for young children. So bring your water noodle and just relax and take in the beautiful scenery.