New Zealand Advice
 

Flying to New Zealand from Chicago is a 20 hr ordeal. Where can we stop for a one or 2 night stay before continuing on to Christchurch?

Auckland?
Stay in the city, take a day trip to Waiheke Island or Rangitoto Island. Other day trips could be out to the Waitakere Ranges Regional Park for a bush/waterfall walk or to Piha beach which has black sand.
Time of year?

Not a whole lot of options, unless you spend a night on the West Coast before heading over - Chicago to LAX is what, 4.5 hours?

I find it's easier to just get it over with in one go.

Breaking up the trip potentially costs more and eats into valuable time that could be better spent on the SI IMO, but stopping in Auckland is a viable option if that appeals to you.

Keep in mind that most flights from the US land in Auckland pretty early, so you might need to arrange an early hotel check in if you opt to stay in Auckland for a few days.

Another option that may or may not appeal to you, but something I've done before - land in Auckland, get a day room at the Novotel at the airport (right across the street) get some sleep and a shower, then walk over to Villa Maria for a nice lunch.

If you do this, I'd suggest checking your luggage to Christchurch and just keeping whatever you need for the break in your cabin bag.

Then catch a early evening flight to Christchurch.

That means paying for two hotels in one day, but it's an option.

Just get it over with. Fly all the way to Christchurch. You'll arrive at a more decent time of the morning. Drop your bags at your accommodation and find a place for a leisurely breakfast. Then explore the city until check-in. At check-in, take a shower and get outside again. Adrenaline will keep you going, along with fresh air and some walking, until dinner. Try to stay awake until at least 7 or 8pm.

In business class or better, do it all in one go.

In coach, split it up so there are no redeyes. I enjoy going via Hawaii and Fiji. One day a week, the Air Fiji flight between Honolulu and Nadi stops in Kiritimati, so you have the rare opportunity to see a raised coral atoll. You are not allowed off the plane, though, unless CXI is your destination. There are nonstops from Nadi to Christchurch (and Auckland and Wellington).