Another option for a Poor Knights liveaboard is Pacific Hideaway (
http://www.divenz.co.nz/) - new owners this year, so I'm not sure what the quality is like as I've not been out with them.
For my tuppence worth, a 4-6 day liveaboard probably won't give you a taste of the variety of diving in New Zealand. My top spots to visit would be the Rainbow Warrior, the Poor Knights, White Island (a live volcano), Pupu springs, the Lermentov and Doubtful Sound.
For the Poor Knights, I can seriously recommend Bluzone (
http://www.bluzone.com) for day trips - the owner will take you to the sites of your choice, whereas Dive Tutukaka (who are an awesome charter) are focussed very much on bulk traffic and you won't get to see the best spots. Bluzone will only go out with a group greater tha four, but I know half a dozen people who are always keen and the skipper puts on a fantastic buffet lunch for $15.
White Island is a definite must! My favourite charter is Dive White (
http://www.divewhite.co.nz)
I have to say, re: Azza's post... water *can* reach 24-25 degC in summer, but you'd probably be wise to expect it to be around 21 degC to be on the safe side.....
If your window is November to March, I'd say sometime after Xmas. The last couple of years have seen some big algal blooms around Nov-Dec which has brought the viz down to around 5-10m at the Poor Knights. Jan-Feb is generally peak season so accomodation and charters (liveaboard or not) will be busy. March has been a great month for the last couple of years - warm water, stable weather and is starting to get quieter.
If you opt for the day trip thing and want a local guide, let me know as I work flexi and often slip away in the week for a dive.