I'm a big fan of the botanical gardens on Hong Kong Island. It's like a little zoo experience in the middle of the city... But the Hong Kong botanical gardens are nothing compared to Tuen Mun Park. This place gives all the hits of an amusement park without the crowds and cost - it's completely free. Want animals? Sorted.
There is a wonderful little reptile house with most of the displays at kid-friendly heights. They've got pythons, vipers, skinks, pig-nosed turtles, massive and very old tortoises... It's well worth a visit alone, without all the other cool stuff the park offers.
After the reptile house, head to the massive playground. Pretend to conquer the castle and besiege the climbing frames as you tear around the 'spinning area' and throw yourself down the Big Slide. It's excellent and big enough to keep the kids entertained for ages. There's also a massive sandpit for smaller kids to kick about in.
You've worked up a sweat and need to cool off? No problem. Come out of the playground and head for the water-play space. I recommend bringing a change of clothes/ swimsuit for this. There are changing areas near the playground. Soak your loved ones by activating the buttons to get the water pouring.
Once you've had your water fight, the rest of the park is lovely to walk around. They have a big designated skate area which is really just some little paths to shoot about on, and a cordoned off section of lake for RC boats which is great fun to watch. Take some lunch/ snacks as food options are limited.
Getting there is super easy. Jump on an E36A bus and get off at the Tuen Mun Town Hall. Go right off the bus, then follow the road around to the left. Go up on the the raised walkway near the bus station and follow the footbridge to the park.
To come back to Lantau, take platform 8 (the first set of steps to the right off the bridge out of the park, the same way you went in). The bus stop is down the bottom of these steps.
Another great local park is Tsing Ti. You can read all about that here.