So a group of 4 of us, younger adults, are planning a trip to NZ and Australia. So far we would be flying into Auckland on October 7 6am after a 23 hour trip and staying on the North Island until either the October 10th or 11th. With our limited time we decided to just stick to the North Island and were interested in going canyoning in Piha, seeing the glow worms in Waitoma, and hiking the Tongariro. However, these things look like kind of far in between requiring longer car rides. We would be renting a car so that would not be an issue, but does anyone else have any suggestions of things/places we should see or does this sound do able?

<<However, these things look like kind of far in between requiring longer car rides>>

How right you are.

With only 3-4 days, I suggest you stick to just Auckland and vicinity, let alone just the North Island, lol.

There is plenty to do around Auckland but also there are some amazing sights to be seen within a few hours of Auckland. Look into the Coromandel, Cathedral Cove, there are plenty of amazing walks around the area as well. It will be to cold to swim at that time of year but some great fishing charters and Dolphin tours.
Or about 3.5 hours from Auckland is Taupo, Waitomo is on the way and there are plenty of activities to do in Taupo. Tongariro is amazing but the travel and the walk will take up the majority of your time in New Zealand. Piha is amazing too, black sand beaches are so different than white sand beaches. I would probably stay around Auckland and go to Piha and maybe a day trip to Waiheke Island for a wine tour. Its only a 40 minute ferry trip.
If your looking for culture, Rotorua is about 3.5 hours away and there is plenty to see and do there, mud pools, luge, buried village. Have fun.

thanks amazing information and help

If you go to Rotorua, I would recommend the zip lining tour there... absolutely fantastic. If you are into The Hobbit, Hobbiton isnt far away from Rotorua. Great tour - really interesting.