We have found the best places for toddler holidays have been Bay of Islands, Rotorua, Tauranga/The Mount, Taupo and around the Hokianga Harbour.
If you are based in Tauranga there are a few petting zoo type of places around and McLaren falls, good for picnicing and walks. The beaches at the Mount are beautiful but are surf beaches so be careful with your toddler. You can walk around the Mount in about an hour, plus there are outdoor heated salt water pools right by the Mount itself and plenty of nice outdoor cafe type eateries. It's just over an hour to Rotorua where there is Rainbow Springs and Farm plus all the geothermal activity. There are also good walks through the Redwood Forest and around the many lakes. Lake Taupo is another hour away again. The Lake is good to swim in, Huka Falls are spectacular and either a five minute walk from the carpark or a one hour scenic walk each way from Taupo township. Nearby we like the one hour Craters of the Moon geothermal walk. There are plenty of heated pools around this area as its the geothermal area but be careful if using natural pools due to risk of amoeba. Napier is about 1.5 hours from Taupo and the main attractions are the Art Deco township, vineyards and if Marineland is still open, this is well worth a visit. You can also go out to Cape Kidnappers and view the Gannet Colony.
Northland hotspots are comprised of Paihia, Russel and Keri Keri on the East and the Waipoua Forest and Hokianga on the West. On the East you can visit the Waitangi Treaty House, walk out to Haruru Falls (an hour), get the ferry to Russell and view the old historical buildings. There are also lots of scenic boat trips to experience the Bay of Islands. On the West are the biggest Kauri trees in NZ in the Waipoua Forest, with buggy achievable walks ranging from 15 minutes to 1.5 hours, plus the beautiful Hokianga harbour with all the little bays and inlets.
For a volcano experience visit Whakapapa village at Mt Ruapehu. The visitor centre is great and there are some short volcanic walks you can do. There are great views of the three volcanos.
Make sure you have a robust three wheeled buggy for your toddler so you can take advantage of the numerous 5-60 minute easy walks.
February is the hottest month of the year but schools have just gone back so the weather should be good, and crowds lessened. Make sure you carry plenty of water and sunblock, don hats and get out of the sun for most of the 12-3pm hottest part of the day.
I would also suggest stocking up on snacks (crackers, boxes of raisens, muesli bars, biscuits etc) at a supermarket as you are a long way from food at some of the parks and walking tracks.
McDonalds ice creams are only $0.60, you can use the indoors playgrounds (out of the hot sun), they have clean bathrooms, and you can fill up your water bottles and change into your swim suit while there. We use the Taupo one daily when staying there as its less than 100m from the Lake itself and provides an air conditioned respite for an hour or so out of the day.