In spring, from August to November, the westerly winds are typically at their strongest – these are called the equinoctial westerlies. It tends to rain more in western areas, and especially on the South Island, at this time, while in the east, warm dry winds can give great cycling weather.
Domestic flights in New Zealand are often cheaper than driving or taking the train, especially if a crossing between the North and South Islands is required.
Riding bikes in New Zealand can be fun, but be aware that because of the geography and small number of people cycling between towns there are very few cycle lanes and limited shoulder space on roads.