I go to Sydney often throughout the year and never had a problem with weather. It is a great city and great people. Be sure to go to Circular Quay and just catch ferries to different places.
I always stay at the Holiday Inn Potts Point. It is a few minute subway ride ( subway under the hotel) to the city, but has the BEST views of the city and harbour. Staff is great. It is in Kings Cross, which can look abit seedy, but it is perfectly safe. I have gotten great rates at this hotel through their website (sixcontinents.com) or Orbitz.com. I have paid as little as US$70.00 for it. Great hotel.
You will enjoy Australia. Don't forget to have the airline get you a visa.