We (myself and 2 very capable boys) have done Waitawheta hut and Daly Clearing hut, we thoroughly enjoyed our nights in the huts and the journey to get to them. Waitawheta our first nice and easy up the tramline. Daly we did from Dickeys Flat campground slightly more difficult and longer but certainly well within our means. What other huts are within a 7 (each way) hour walk preferable from the Waikato sides. I have looked into theTe Rereatakuhia and Hurunui huts. Main thing for me is safe(ish) parking.
Te Rereatukahia is definitely a great hut, and if you just climb about 15 minutes from the hut to the nearest hill top (on the way to Wahine rock, point 735 on the map) you will get amazing sunset and sunrise (if weather is clear of course). Parking at the end of Hot Springs Rd should be quite safe, there's homes nearby and there was quite a number of cars there during the weekend. This way you can do some kind of loop.
If going there in winter, keep some water inside the hut, last year the taps were frozen in the morning!