Across from the ferry terminal in central Auckland are several tour companies that operate city tours. I took one last month on a brief stopover with Scenic Tours. Pickup around 10 am at your hotel, drive around the city seeing some sites, then they drop you at the museum and give you a couple of hours there, then a little more sightseeing and back to your hotel. I think the cost was around NZ$60?

Waiheke Island is a nice day trip too. A company called Amanda's Tours (and others, I am sure) do winery tours around the island.