A world-class city
It's hard to say whether Sydney or Melbourne is better, but Sydney definitely has a lot to offer for anyone. The weather was nice, even in summer it was a balmy 27-29 C. Many great places to eat, many great sites to see. I really liked Bondi beach, but Manly is pretty cool, too. If you can, do travel also to the Blue Mountains and Jenolan caves, very beautiful scenery, and it's a nice change of pace from the urban sprawl of Sydney. Just be prepared for how expensive things are in Oz in general.
Insider Tip:-Definitely invest in a reusable water bottle, will save you a lot of money and there are numerous public water fountains and filling stations, especially at the beach.
-Save more money by taking the free walking tours, www.imfree.com.au. They do two tours in Sydney: a general Sydney tour and a tour specifically for the historic Rocks district. Not totally free, I guess, because they do ask for tips at the end, but still not as expensive as official tours.