Not sure how far from home you're prepared to travel, but here goes anyways...
1)
Featherdale Wildlife Park at Blacktown is quite popular with primary school age kids and gives them good "hands-on" experience.
2)
Not sure what it's like with the new owners, but Calmsley Hill City Farm
http://calmsleyhill.com.au/ could be worth looking at too. It's basically adjacent to the Western Sydney Regional park that has good cycling tracks (was the site for the Sydney Olympic MTB events), can get access through to the M7 cycleway. Hills might be a bit tough for younger kiddies - but IIRC your's is maybe the right size to have a crack at them.
3)
Sydney Olympic Park would make a good day out. There's a number of interesting environmental projects and plenty of "bush" and mangroves to go bird-watching etc.,. (Newington Armoury is best for the latter). Bikes for hire, or you can take your own and ride your way around the very kiddy-friendly bike tracks. Bicentennial Park would be a good place to start. Decent coffee at either Lilies in the Park, the Newington Armoury Cafe, or some of the cafes around the railway station/ANZ stadium area.
4)
Not quite a "bush walk", but the Coast Walk from Bondi to south of Coogee beach is an excellent way to get the sting out of young legs (can get a bus back if they get too tired). Fresh air, and best scenery in the world. Lots of options for lunch and refreshment at the various beaches along the way.
5)
Similarly, the Spit to Manly walk is a bit more rugged, but also great fun. Other north-siders can probably fill you in on details for that.
Cheers