When is the best time to vacation in New Zealand, i.e., moderate temps and few people?

If you want to combine those two elements then, essentially, you want to travel to New Zealand slightly out of season. High season tends to stretch from Labour day (October) to Easter (March/April). So just before and just after would combine the two. Once you move into June July and August (the winter months) then the weather gets colder, but not necessarily less stable (i.e. rainier). The dryest month is February, but this is in the high season and the crowds can be frustrating. Please remember though, that New Zealand never gets insufferably hot or cold but, with its increasing popularity as a tourist destination, the high season months of October through to March can get very congested around the main tourist areas and on the well publicised walks. But if you like going off the beaten track there is always a remote place waiting to welcome you.

I'd vote for November til mid December (end of spring), and Feb and March (end of summer, beginning of autumn). Kids are off school mid Dec through the end of January so that's a good time to avoid. I've never found tourist spots to be particularly crowded in spring and autumn either.