I'm on my laptop Michael and all my good junk is on the desktop, I'll try to do a better map later although I am not a map person so if someone wants a go at it please do.
puddin, I am a map person and will see what I can do. However, the map you provided tells everything that's needed except the distances. I can't find one with distances, so here is a slightly different version of the map you provided:New Zealand North Island Map
I can center the map on the part west and north from Tauranga but that is not the way it comes(although the resolution is good the way it comes). You have to manually take the control up about 6 times until you are have Hamilton on your view. Then you pan east once until Tauranga is on the right edge.
What that shows is two routes for getting from the Auckland area to Tauranga. The one you showed is:
route 1 south to
route 2 east
after a small distance 2 turns left and route 27 begins
follow route 27 to Matamata and take route 24 there(it cuts the corner)
take route 29 north from its beginning out of route 24 and follow 29 into Tauranga
A probably better alternate(we would need a native such as Kiwijay's parents to say; I will ask my brother-in-law) is:
Continue route 2 east until it turns southeast and then east all the way to Tauranga (and further to Te Puke).