Living on the Central Coast is often a personal pain point for me but one area where it does excel is the variety of hiking trails and national parks that are often very suitable for young kids and always very scenic.
Here are some photos I took on my iPhone across two separate visits:
The walk itself is pretty easy - flat for the most part other than some stairs here and there and the trail is clear and well maintained. There is a lookout approximately 15-20 minutes into the trail (coming from Killcare) which makes the visit worth it even if you were just planning to go there and then head back for the day.
Getting there and parking is painless other than a negligible parking fee. There are well maintained facilities adjacent to the parking i.e. toilets, BBQs, benches, grass area to have a picnic, etc. Some letters on the parking ticket machine weren't working for me, so I wasn't able to enter my correct license plate number, but I doubt it matters much as long as you pay for the ticket and show it on your dashboard.
One issue I did have was that on both of my visits it was quite busy (you can almost always see at least one other person or group up ahead) and the trails get pretty narrow in some sections, especially in the later half. If your kids are only between 2 to 5 years old like mine and walk slowly without watching where they're going, this can make for some awkward interactions on those sections, but overall there is ample room to walk to the side and let others pass without collision. Both times I went it had been raining on-and-off in the week leading up to when I was there which made the trail extremely muddy for the last third or so as well, so I would recommend delaying your visit if there has been recent rain and you're planning to complete the entire walk.
Great for a day out or just a quick walk to the lookout and back before heading down to Empire Bay Tavern for lunch.