My family uses Uber,except travelling from the airport isn't as convenient as going from the city to airport. I suggest using a shuttle service with Super shuttle having a permanent base at the airport. Cost effective, reliable and convenient.Edited: 06 February 2018, 15:30
Yesterday I took CheapCabs from the airport to downtown Auckland. I just looked for the first CheapCabs taxi in the line. Good ride, good driver, and cost just NZ$ 42.
I find Auckland public transport difficult. There is an Airport shuttle that is about $17 one way or $32 return trip that only takes you into central Auckland. You can get off at the last stop which is the main transport hub and find a bus to Ponsonby.
There is no one bus from the Airport to Ponsonby. You will probably have to change busses several times and walk between stops. Of course this will still be cheaper. Here is the URL for Auckland Transport's trip planner. https:/… you can put the exact address in to see if you can find a bus from Britomart to a stop near your hotel.
If there is two of you travelling together, this is getting up near $40 anyway so you might be better to look for an Uber. Drivers in NZ are police vetted, and have to have a passenger service licence and a special warrant of fitness on their car so you should be safe. make sure it is not rush hour when you are coming into the city though.
From memory, discount taxis are really cheap and reliable. You can book when you arrive.09 529 1000 or book online.