Have you been to Auckland before? If you have and liked it, then I guess 7 days there is your personal preference. If you haven't, I would say 7 days is way way way too long in Auckland. I would spend 2-3 days in Auckland and spend the rest (and maybe some of the extra 9 days) in the South Island or Wellington (which I hear is nice but have never been). You mention you're a big city person, but honestly, the reason to go to NZ is to get away from the big city.

And how about Sydney, since you've only been to Melbourne, or the GBR area?