Yes,there are parts of the North Island that are very nice.
Some of my favourite places are the beech forests of the Urewera National Park,near Rotorua.Theres a little lake called Waikareiti and a hut on the far side,from which a track goes up to the highest point in the park.Theres an awesome 'Goblin' cloud forest up there with huge gnarly trees covered in long beards of moss,like something from Middle Earth.
The volcanic plateau in the centre of the island has many interesting thermal areas,notably at Rotorua and around Taupo,& there are some great mountains there where you can ski in the season.
Mt Taranaki,or Egmont on the West Coast is beautiful,and then theres the Bay Of Islands in Northland,and of course the Coromandel Peninsula.
I think my favourite parts of New Zealand,though,have to be on the West Coast of the South Island,from Golden Bay in the north,right down to Fijordland in the south.
I find the North Island a bit crowded and too 'cultivated'.
I do like my forest

Cheers
Steve