Auckland airport around midnight will be reasonably busy with the evening flights from Australian ports arriving. Baggage, customs and immigration should be quite smooth. As others have said, no fresh food to be brought in though.

In the arrivals hall there are a couple of small convenience stores that have chips, soft drinks, cakes and some other basics available. I usually grab a couple of snacks when I arrive. You could also grab a bottle of wine from duty free on arrival if that takes your fancy.

A taxi from the airport to the city will set you back about $100NZD and should take about half an hour.

The Grand Mercure might be another hotel worth considering. It's at the bottom of Queen Street, half a block from the waterfront and at the posh end of the shopping strip.