Auckland International Airport is the country's hub, and easy transportation options exist for the 45-minute drive into the city. Visas are not required for U.S. nationals staying less than three months. Note that New Zealand has very strict quarantine rules, so avoid bringing food if you want to avoid an instant fine. Cruise ships are an ever-increasing option, and stopovers in Auckland are on the itineraries of P&O, Princess, and Regent Cruises, to name just a few.
While Auckland’s public transportation system is gaining favor with locals, it is a far cry from a metro network. Trains are limited (none cross the harbor), and buses are hub-and-spoke based (rather than point-to-point). In downtown Auckland, the Link bus service has three routes circling the greater and inner CBD (Central Business District). Taxis are plentiful, and all the major rental-car companies have a presence at the airport and in the city (remember that New Zealand drives on the left). Auckland is not built for cyclists, and there are very few cycling lanes. Walking is easy if you're not going far, and the most enjoyable way to sightsee is on a Fullers ferry.