For those with experience flying around New Zealand, any recommendations on particular aerodromes to visit?
Depends on what your interests are.
The Bay of Islands area is nice, since you're most likely arriving and departing from Kerikeri, stay at Paihia or Kerikeri for a day or two and explore the area take a day cruise around the islands or a bus trip to Cape Reinga.
The Coromandel area is worth a stop. Whitianga is probably the best spot to base yourself, good airfield, good beaches nearby etc.
Taupo is a good place to see geothermal activity. Rotorua is better known and but Taupo is a nicer place to stop. The closest I can think of in OZ to Taupo is Jindabyne except there's not geothermal stuff at Jindabyne.
Omaka, (Blenheim) great place to see the Marlborough Sounds from and there is a fantastic aviation museum there.
If you're into gliding or not Omarama is a neat place to stop with the hotel in the airfield.
Queenstown or Wanaka. Queenstown is more touristy Wanaka is more laid back and I think a better climate. Both worth visiting.
Croydon Aircraft Co. at Mandeville is a must if you're into de Haviland aircraft.
A trip up the West Coast of the South Island is a must stopping at Hokitika or Westport or both.
That should keep you busy. for a day or two.