Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Auckland to Gerald R. Ford Intl as you normally would.
The rainfall in Auckland is generally more than the rainfall in Grand Rapids. This will continue over the next 8 days.
Expect the weather to be around 29 °C on average in July. As the temperature peaks, try to get your plans done early, as flight price and availability will have an impact on your travels. The climate in Grand Rapids is generally hotter than in Auckland.