Planning travel to New Zealand in mid-October for around 9 days - in North Island

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I accompany with my friend going to North Island of New Zealand and will be staying there around 8 days in mid-oct. We want to visit Auckland, Rotarna, Waitomo and Wellington. Would someone suggest the sightseeing places and activities, cheaper hotel and transportation in details? Pls note that we won't drive by ourselves, it depends on train and bus. Thanks.

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