New Zealand offers a lot of activities, especially for the adventurous kind. You can bungee jump, ski and snow board, relax on the beach, go for a bike ride, take a 4 wheel drive adventure, ski dive, surf or simply, shop! Most adventurous activities are available in the South Island, whereas North Island offers the charm of the big cities, some great shopping as well as some uniquely New Zealand attractions, like the Maori village in Rotorua.
The best way to travel around New Zealand would be in a rental car. Most New Zealand cities are very well connected with the main motorways and traffic is usually not a problem. There are information centres in most tourist areas, providing useful travel information, maps etc.