I would recommend checking out the Whangaparaoa Peninsula, which is around an hour’s drive north of the city center and connected to the city center by ferry. Near the end of the peninsula is the Gulf Harbour Marina, which has a great freedom camping location right next to the waterfront! You will pass plenty of shops on the way to the freedom camping parking, so stock up before getting to the marina. There is ample freedom camping parking with toilets nearby. This is right next to the ferry terminal, so those wanting to explore the city for a day can leave their vehicle and catch the 45 minute ferry to the city center! There is bus service that goes to this marina, but that would be much longer than just booking a return ferry ticket. Exit the ferry at Pier 4 in downtown which is walking distance to Britomart (train and bus service) and near Queens Street.
The other is the Rosa Birch car park in Pukekohe. Nearby train service goes all the way from Pukekohe to Britomart in the city center of Auckland. A good list of the regional freedom camping sites can be found here.
Auckland City Council can change the availability of any freedom camping sites, so check their website to find out the latest information as there has been reports about them opening up various parks across the city to self-contained vehicles for a maximum of 2 nights per month.
We were able to hire the campervan for almost 1/3 of the peak season cost at just $38.20NZD per day! (Peak season is Nov-Feb for NZ when campervan prices shoot up). You can get great deals on campervans outside of these dates, or possible consider a buy-back campervan if you will be in NZ through the busy summer season.
Insurance with $2,500 or higher deductible is usually included with NZ campervan hire. I found it cheaper to buy travel insurance (with rental vehicle cover) than dropping the deductible lower through the campervan companies. That way our flights, belongings, healthcare and campervan were covered. The smaller vans can be even cheaper at $20 or $25 a day if not traveling in peak season. We usually use Lucky Rentals, but shop around for the best deals on the dates you need.
Tip: Download the CamperMate and Rankers apps which list most of the freedom camping spots around New Zealand.