We will be heading to NZ for 5 days/4 nights and Sydney for 7 days/7 nights in late August on a Qantas award ticket. Before anyone asks, I know the trip time is limited, but we can't leave our 2 year old at home with grandma any longer than that.
I need some advice from FT's experienced travellers on how we can maximize our limited time.
New Zealand: We are flying into Auckland on a Monday and then flying on to SYD from Auckland on the following Friday. Should we just see the Auckland area and Waikomo/Rotorua or is there time to see some of the other North Island areas? We will be renting a car. Any hotel recommendations would be greatly appreciated as well.
Australia: We are flying into SYD on a Friday evening. I have booked a 5 night award at the Sydney Renaissance and left the last 2 nights open for a side trip (maybe the Blue Mountains?) What other can't miss sights are there around and in Sydney (besides the obvious well-known ones)?

Thanks in advance for your help and I'll be sure to post a detailed trip report when we get back.