Looking for a Challenging day hike near Auckland

I am writing from Texas, my son is a martime merchant Marine cadet from Texas A&M Galveston who will be arriving 7/28 in Auckland on the CalMaritime training ship Golden Bear and will have 24 hours of liberty. He and two freinds are looking for a challenging day hike ( they like to climb up on top of tall things like mountains) and had theri sights set on your Mt Nguarahoe but I researched that as a no go for a day hike, in particular at this time of year. I am trying to help them seek a reasonable alternative as hey have no internet access on thier ship, only email and found your forum. Can anyone over there advise and recommend a suitable alternative destination they could drive to from the harbor in Auckland, take a fairly challenging and interesting day hike then return in the evening. They are all in good shape with hikng, or 'tramping' expereince as Eagle Scouts in the rugged SW US. I di some research and came up with Mt. Te Aroha, the Hunua area as well as the Husaua range. Do any of these sound like good candidates or does anyone have other suggestions. Any thing to keep them off Nguarahoe this time of year. I may have to come back with him ( in the summer) for that one as it looks very interesting. If you are ever in Texas be sure to visit our Big Bend. Thanks, Steve