Routeburn is pretty awesome. It doesn't end on Milford Sound like the Milford Track, but the sound is just a short bus ride away. Routeburn wasn't buggy at all, and I hear the Milford track can be a bit buggy. It's also easier to reserve, but still need to do it months in advance. And tying it together with the Greenstone or the one that goes north to Lake McKerrow could be fantastic.
If you decide to head north, the Bay of Islands is nice, warm, and subtropical. Heck, that time of year, all of New Zealand is warm, and the landscape and people are pretty nice any time.
Regarding flights, some friends got a smoking deal on shoulder season flights through Fiji on Fiji Air. I don't know if you'd get the deal during the high season, but it's worth a look. The only bummer is the layover in Fiji........
Finally, I hear exchange rates are pretty favorable right now, like 1USD = 2NZD. That's practically mustachian. Enjoy your trip!