The distance from Auckland is about 6 km (by ferry).
Take the Waiheke ferry from the wharf by Auckland's Ferry Buildings. John and Clare Campbell have a private naturist place at Surfdale - only five minutes away from Little Palm Beach, but they are happy to meet the boat, drop you off at the beach (or accompany you there, if you wish) and return you to the wharf.
Guest facilities include a deck and spa pool. If you are staying more than a day or so, other beaches to visit might include Onetangi (east end, which is a direct trip from the gate) or possibly Hooks Bay which is only a five minute walk away and normally deserted, except maybe on peak season weekends. Please contact via firstname.lastname@example.org or contact: 021 813 522 beforehand, as they may well be booked out during the season - especially at the weends!