PS Around Rotorua there are some very beautiful volcanic lakes

The most famous ones are the Green Lake and the Blue Lake - they are right next to each other, not too far from Rotorua.

Also Lake Taupo should deserve yourtime - probably the most beautiful lake in North Island. Nearby there is a nice trail along Wairaki River, and see Huka waterfall. You can also do the exciting and famous "Shotover" jet boat ride. I believe the Jet Boat ride originated from Huka near Lake Taupo.

Hamilton has not much to see.

Be sure to visit the Te Papa Museum at Wellington.