Hi, 7 days is plenty of time if you want a whirlwind trip. North Island is basically - that, an island. Drive down one coast, and kind of back up the other side (but more or less through the middle of the island). Auckland - Rotorua - Taupo (overnight in Taupo), Napier/Hastings - great wine -(Hawkes Bay) stay there overnight, Wellington (lots to see on the way down in little rural towns) and a very nice wine region just out of the Wellington (Martinborough) - overnight in Wellington. Then just drive back up - Palmerston North, New Plymouth (overnight), volcanic plateau (Tongariro, Ngarahoe, Ruapehu mountains) Taumaranui or Turangi overnight, Waitomo Caves (personally I think they are over-rated) Then back to Auckland.
I'm a New Zealander, and when we have overseas guests we tell them to give Rotorua a quick visit, and go to Orakei Korako - its a bit off the beaten track, but the mud pools and lakes are far superior to Rotorua. Taupo has beautiful views of the lake and to the mountains.
Really, don't plan too much, just see where you end up, that's the best kind of road trip. If you miss out on seeing something, you might see something better (and you can always come back again another time).
Have a great time. Enjoy our lovely country.