Good 2-3 day trip on North Island August-Sept?

Hi, I'm looking at options to do a good 2 to 3 days trip on the NI next month or in september. I have good gear and can handle temperatures down to -10°C with my two down sleeping bags, have goretex overtrousers and stuff, but no snow shoes / crampons / ice axe and don't know to use them so I'm not looking for heavy snow conditions as I won't be comfortable with that. Can Tongariro Circuit or Pouakai circuit in late Sept. be OK or would it be too soon? Something else? Shouldn't be too far from Auckland as I can't take more than 1 or 2 days off from work. And if you have ideas of nice overnight walks in the Auckland area I'm open to suggestions, I'm trying to get out every weekend but it's sometimes hard to find something I haven't done yet :) Thanks!