I think your open days will be well and truly consumed if you haven't been by tiredness and as much as you could easily spend more time on either island, with limited time you've probably got as good a split as what you can, there being things you'll miss out on, but not too much that can be done about it without another couple of weeks.

What you need to realise is that NZ does not have any US interstate highway system, their SH1 as it is called being a single carriageway road just about the whole of its length other than about 100 km. between Auckland and Hamilton and then once away from SH1, the roads will generally be narrower and more windy in many places with only blessing being that you can expect to have very little traffic compared to what you'll be used to in the US.

BUT BE AWARE OF  

. blind curves in hilly terrain and cutting corners like local drivers and tourists may well do, and just remember which side of the white line you ought to be on - if you're too close to the edge of the road it could well be because the steering wheel is on the right hand side of the car and you have the car on the right hand side of the centre rather than on the left.

. one way narrow bridges, there being a signage system to become aware of on who has right of way - it being easily enough understood and you'll have a white line across the road and possibly a stop sign if you have to give way - but use great caution anyway, and get across quick even if you have right of way.

. taking your eyes of the road because Mum says "Oooh, look at that lovely lake" - just up the road there could be a pull off or parking bay for a lookout.

As a general rule of thumb, I wouldn't be planning on any more than 40 -45 miles/75 km. being covered per hour on average, and a bit less in some alpine/lakes sections - some planning ahead -http://discovernz.co.nz/driving/smlcalc.html and that came from http://www.travelplanner.co.nz/ but distances link was not working - does with Ctrl.

Do not forget the apple if you get one on the flight and decide to keep it for Ron and try and find enough time between getting through customs (turn to left for Vis info) and hopping into the rental to pick up some maps and info, all regionally based, all free.

And then if you do start to feel Jet Lagged Lousy Drowsy, do pull up somewhere for a nap rather than become another holidayer statistic.