Cool. Well I’d hire bikes in Rotorua if your going thru and the Christchurch MTB park. Makara peak in Wellington is good riding but the hire bikes from nearby suck so unless your gonna rent a better MTB from the city and ride/drive to the Park I wouldn’t bother.
Walking wise can do a day on the Queen Charlotte Track, take a water taxi from Picton and get picked up further along the track.
Also recommend a days walk on the Abel Tasman also use water taxis, can have lunch at Awaroa Lodge that is on the track.
On both those tracks you can camp/book accommodation and stay a night but that time of year I’d be looking at booking any DoC ( Department of Conservation) sites or huts now.
Do a walk around Aoraki/ Mount Cook, even the 30min walks get you up pretty close to the glaciers, better than the West coast one’s in my opinion.
The walk up mount John from Tekapo is great on a nice day and a fairly easy walk with coffee at the top and great views.
A walk along the crater rim walkway is pretty sweet in CHCH if you’ve got nice weather, great views of the Harbour, City and mountains.
There are heaps of 2-3 hour walks around Arthur’s Pass and Lewis pass to.
Maruia hot springs are better than Hanmer if you want something like that