The circular quay and Rocks area is a great place to base yourself although will obviously be extremely busy at New Year.
I ditto Papillions suggestion of the Shanri-la which has a lovely club level lounge with great views of the bridge and opera house, so even if you do not have this view from your room it might be a good idea to have a club room. The hotel is up a fairly steep hill but great for working those thigh muscles !
I would just check on the New Year policy at any hotel you book, as there may be restrictions or extras to pay. In Hong Kong both New Years mean hotels and venues find extrodinary ways of ‘making you pay’ for a great view.
Sydney is fab x enjoy