There are various optional activities can be added to your pre-planned itinerary, especially for the free days. We need to understand your needs and wants better to be able to suggest the suitable ones. We need to know your age, your fitness level. Are you into adventure activities, soft adventures, wine tours, lord of the rings filming sites, cruises, etc?
You can check the optional activities for each region here:
NZ Tourism.com New Zealand Tours, self drive & seat in tour packages