If you are going to be on the Northern beaches , here are some things you can do for free
The Manly to Spit Walk (or vice versa) is excellent with great Harbour Views, quiet beaches for a dip , aboriginal carvings etc.
Also North Head has great lookouts and walks and is a good place to watch the sun go down with a picnic - reasonable chance of seeing Echidnas or Bandicoots on some of the walks to the Barracks from North Head too.
There are lots of other great walks too, like the Dee Why to Curl Curl coastal walk , or Taronga Zoo to Chowder Bay with beaches and playgrounds galore to stop at.
Snorkelling at Shelly Beach is fantastic, it's a marine reserve with lots of colourful fish and rays, turtles etc. you can see most things in very shallow water
here's an example video
If your children want to see Kangaroos in the wild rather than in the zoo , then Ku-ring-gai National Park at the north end of the Northern Beaches is a good option , guaranteed at the Basin campground or near the visitor centre on Bobbin Head road. If going to the Basin you can combine it with a visit to West Head and Palm Beach with the Home and Away Surf Club building.
A visit to Cockatoo Island in the middle of the Harbour is really interesting too , you can do it on a regular ferry from Circular Quay , it's got tunnels through the island, art installations and it even has a permanent camp-site so if you stay overnight you wake up to the City coming to life.
Literally there are hundreds of things to keep your kids entertained - hope you all enjoy it