Gday, yep the Tongariro Crossing in June is a mint idea, you will likely have the track to yourself!! Get a good day and it is sweet as.
- Ngauruhoe is a good objective, though you will likely need crampons and an ice axe for some likely sections of ice.
- Tongariro is a small trek to the crater.
- Ruapehu is the North Islander's winter playground. Here you can do anything from snow plods to the summit and stunning crater lake, take on water ice to WI4, traverse any or all of the 12 'summits' upto NZ grade 2+ or if there is enough snow, do the Pinnacles traverse (Whakapapa side).
PM me if you would like more info. Also highly recommend mountainz.co.nz. Some good peeps there too.