There's also a dam just north of Taupo that gets released around every lunchtime. It's cool. It's about a 10m drive north.
The geothermal walk called Craters of the Moon is wicked - you do have to pay but it's not much. It's a good, pretty flattish walk that can take a couple of hours if you're slow and look at everything along the way. In that same area is horse treking - it costs, of course, but it could be within your budget.
The Honey Hive near the Huka Falls is definitely worth stopping in at - it's free, you can learn about bees and taste test honey. Along that same area near the prawn farm is a geothermal activities centre where you can learn about volcanoes and stuff. The Huka jet is cool, but I think it's around $60-70. The prawn farm is also pretty cool, you can go fishing for your own prawns. Awesome.
If you can, drive around to Kinloch and spend the day at the beach over there. There are lots of walks in that area too.
Right opposite the turnoff where you go up to De Bretts and across to Napier is a hotel and little road. If you drive down the road and park at the bottom, then walk around the lake to the right past the rocks. Bury your feet in the sand, and it's nice hot water and sand. A perfect way to spend an evening with some fish and chips, but make sure to bring your insect repellant.