Things may have changed a bit since 98 when we celebrated NYE in SYD but I'm sure you will have no problem finding plenty of pretty things to look at down in the harbor area! We were living in Perth at the time but decided to spend NYE over on the other coast (I was expat on assignment for 1 year). At the time I was 27 so not too much older than you. We made a few errors in judgement that I'd like to pass along. We were actually using SYD as a 1 night stopoff on our way to NZ. We booked a great restaurant called "The Waterfront" overlooking the opera house and harbor and planned to fly in early in the day, change clothes at the airport, go to dinner, stay up all night and hop the first plane to Christchurch, NZ (ok, we were young and stupid). On paper the plan could have worked. Problem was, we arrived a little late and found a line not less than 1/4 mile long for taxis. We waited a while and realized we wouldn't make it to dinner so we took a bus which traveled quite quickly until we got about 2 miles from the city centre when traffic stopped. We schlepped it the rest of the way on foot (my poor wife in her 2" heels). We ended up having a wonderful dinner and very much enjoyed the fantastic fireworks and procession of 'floats' on the harbor. There's lots more but I've probably already bored you so what I wanted to tell you is that you can't go wrong in SYD as long as you are ok w/ lots and lots of people and virtually no chance of getting public transportation. If you have a place to stay within walking distance, you'll have a great time. Don't let my friends in my beloved Perth hear this, but SYD has more energy on NYE than Perth. ....Oh yea, we did end up making it to the airport on NYE after we wore out at around 2am and after walking at least 3 miles, taking the subway, and a taxi. Problem was, at that time the SYD airport wasn't open all night (not sure if it is now), so we ended up sleeping for 2 hours on a stack of the-next-day's newspapers - but we looked magnificent! It was a helluva lot of fun!
PS. Whatever you do, don't leave Oz w/o going to Perth and visiting the beautiful Margaret River wine region. Heaven...even for a 23-year old looking for 'scenery'!

PS. I'm sure you'll get a million opinions on this one, but I'd say skip Auckland and jump right to the south island. At your age, you'll love Queenstown and there are tons of young people there to meet. Not to say that you wouldn't like Auck but on your limited schedule and with what you want to see, you have to trim some of it out. Check into Oz and Kiwi Experience www.kiwiexperience.com.