Ohakune railway station: The station is in the Junction/upper town, within walking distance of many lodges. The Northern Explorer links Auckland and Wellington on a limited, roughly three-days-a-week schedule; it is scenic but not a flexible local transport service. Expect roughly NZ$100–250+ one way depending on fare and season; check the operating days before building a trip around it.
Auckland Airport: Rent a car and drive via SH1 then SH49: about 4½–5 hours in normal conditions, plus stops. This is the useful option if you want ski-field access or walks beyond town. InterCity services are the car-free alternative via Auckland, but are a long travel day—about 6½ hours from the airport in the quickest published routing and roughly NZ$90+ one way.
Wellington Airport: A rental car is the cleanest transfer: allow about 3½–4 hours to Ohakune via SH1/SH49. Car-free, get into Wellington and use the limited Northern Explorer service to Ohakune when its timetable works; otherwise buses require a long, connection-dependent day. Do not assume there is an airport-to-Ohakune shuttle.
Palmerston North Airport: Useful only if its domestic flight schedule suits you. Hire a car for the approximately 2–2½-hour drive; InterCity has a daily Palmerston North–Ohakune service, but you must first get from the airport into town and work around its timetable.