Air New Zealand complaint: Flight cancelled for sisters wedding in New York seeking compensation

Our flight from Auckland to JFK was cancelled 29th April. We were told customer service would look after us:
a worthless $90 dinner voucher for a hotel restaurant that had already closed when we arrived – the alternative arrangement a sandwich snack box!!!
we are to be checked out at 11am what are we meant to do until our flight at 20:15 tomorrow? We are advised we would not be kicked out of the hotel the hotel has advised us we have to cover any late check out. This is not good enough.
the whole reason we flew AirNZ was for the sky lounge due to chronic injuries I sustained following a car accident. we have been advised we will not know our seating until we check in tomorrow at the counter. Not good enough.
as if this is not bad enough we are now missing preparations for my sisters wedding in New York.
please advise me who I speak to about seeking adequate compensation for this inconvenience