Road riding is always an option. I've always felt sorry for bike tourists with their bulging panniers trying to make it up a mountain pass. However, there is only one road through most of the places you will be visiting, so you are guaranteed to meet someone at your hotel who is driving through your next destination. You can give that person your panniers and travel unladen. In general, New Zealand does not have the police state apparatus that we have here-I didn't see a single speed trap on the South Island, for example.
Bookstores sell good mountain bike trail guides bike shops often have good information.
You are guaranteed of good riding around Queenstown, the tourist mecca in the SW of the South Island. Bikes are allowed and you can stay overnight at one of the huts. Wilderness travel in New Zealand means never having to carry a tent or mattress. There are magnificent helicopter-supplied huts spaced a few hours walk apart wherever there is a trail. If your legs are sore, rent a sea kayak and poke around the Abel Tasman coast with or without a guide.