This page gives you approximate driving distances and times between towns and cities in both the South Island and North Island of New Zealand.
To travel between the North and South Islands you will need to take an interislander ferry between Wellington and Picton - the actual journey takes about 3 hours but add a couple more hours to take account of check-in time and unloading.
It is really important to note that in New Zealand, the roads are often narrow and winding - often up and down mountains. For that reason, the travelling time is often much longer than you would first estimate given the actual driving distance.
For example, the driving distance is just over 300 km between Christchurch and Blenheim. You might imagine that if the speed limit is 100 km/hr, that you could travel this distance in just over 3 hours. Wrong - it is more likely to take you 4 1/2 hours. The actual driving distance between Wellington and Taupo is 380 km and it takes 5 1/2 hours in a leisurely drive.
We have used the driving distances and travelling times in the following pdf files as they are easy to read and the times are realistic for a campervan driver - they also take into account time taken for short breaks.