Yes, you can use public transport to go to the Spaceships depot in Auckland.
From Auckland airport: bus 38 to Onehunga (Train Station or Bus Interchange), then walk 15 minutes to our depot (1km).
From the city centre (CBD):
take the Onehunga train to Onehunga station. This train now departs from New Market station so you will have to take the Southern Line from Britomart and change trains there. Then walk 15 minutes to our depot (1km).
take bus 30 or 309 to Onehunga Bus Interchange. Then walk 15 minutes to our depot (1km).
Walking from Onehunga Train Station or the Onehunga Bus Interchange is a nice & easy walk (flat terrain). The easiest way is to walk via Church Street. Follow Church Street until you see Alfred Street on your right. Turn into Alfred Street, cross the train line and you will see the Spaceships Auckland depot on your right.
See for more info about the Auckland depot and how to get there.