If time is not on your side and you are not one for endless research, it is highly likely that you will be looking for destination Sydney to be succinct and to the point.
Let us start off with actually getting there. Your best bet will be to try and book flights in the Australian Winter. June and July can often offer the best deals. If you would prefer to catch their Summer - keep a sharp eye out for sales through the major airlines, when you will find the very best deals.
Accommodation wise, book hotel rooms that are a little outside of the City Centre. You should definitely steer clear of the hotels that are located close to the main tourist attractions (e.g. Sydney Harbour Bridge) as these attract a huge premium.
Getting around Sydney is actually very easy: there are regular buses to Bondi Beach and water taxis out to Taronga Zoo (which I was actually very disappointed with!). Sydney Harbour Bridge and The Opera House are both within walking distance of each other; as are all the other main attractions in the city.
Climate wise, you can expect the Winter temperatures to be around the low-teens degrees Celsius in Sydney. During the Summer expect daytime highs to hit the mid- to high-twenties degrees Celsius. Rainfall is fairly consistent throughout the year and Summer thunderstorms can give you an absolute soaking.