I honestly wouldn't bother to go to Sydney just for the opera house, although it's possible that you'll have to fly through Sydney anyway. I'm not much of a big city person either, but I've enjoyed wandering around Sydney. There are some very nice gardens, and the scenery around the harbour is great too. If you're interested in the Sydney Harbour Bridge, you can do the very expensive (but so worth it if you can do it) Bridgeclimb, or the good value climb up one of the pylons to a little museum and views over the harbour. If you really can't find 4 days worth of stuff to do in the Sydney, you could hire a car and check out some of the surrounding areas. A lot of places you can probably even get to on a train if you don't want to hire a car. There's Bondi and other beachy places, the wine region north of Sydney, and the Blue Mountains to the west. PIO has written a short TR on the Blue Mountains and they look fantastic - I'm definitely interested in checking them out some day.
I don't think it's worth going to NZ for just 4 days. It's a big place and there is a huge variety of scenery and things to do and see. If you do decide to go, I would try Queenstown instead of Auckland, and use it as a base for short day trips in the area. Air New Zealand is a great airline if that's what you decide to do.
If you're thinking of doing Fiji, I would do it on the way back. It would be a nice way to break up the long journey home and have a few days of R & R on the way home.