If you are looking for a free day out that will wear out the kids try the Lake Ngaroto walkway. Just 10 minutes from Te Awamutu CBD it offers an easy all-weather track with views of the lake and Mount Pirongia interspersed with bush areas.
I recently took my 2 children aged 4 & 6 and the family dog (dogs permitted on lead) and we set off one sunny afternoon. It was a great way to spend an afternoon with the kids as we talked about what animals would live where as we passed different sections of the lake and swamp and spotted different types of birds. The new track is wide and easy walking with only one small section still slightly damp underfoot. However, I had underestimated the length (despite reading about it on many occasions), not realizing quite how big the lake actually was, and the kids struggled a little to finish the 6km walk. However, with the newly widened track bikes are now permitted (anticlockwise direction only) and next time I would take their bikes to give them an easier trek. All said and done a great asset for the Te Awamutu/Waipa region and something I will definitely do again.
For more information visit: http://www.stuff.co.nz/environment/77340632/Upgraded-track-around-Te-Awamutus-Lake-Ngaroto-opens