Catch train to Circular Quay and the ferry for a day on the harbour or a Manly ferry for a day at Manly. catch City Circle train to St James station and walk to the Art Gallery of NSW. Walk down George St to the cinema precinct for movies and then onto CBD for shopping.
I would recommend that first of all you walk to Sydney Central Station and buy an Opal card and load it with some money to enable travel on Sydney's public transport (buses, most ferries and trains). Catch the train to Circular Quay and from there you can take a ferry to Taronga Park Zoo (which has some good views too). It's a great zoo. Another trip is to take a ferry to Manly and walk along the mall to Manly Beach, there are lots of cafes and shops. Bondi Beach is another must see and accessible using your Opal Card. There's a great walk from Bondi Beach along the coast to Coogee beach (you don't have to go all the way unless you want to. You can even use your Opal card to take a ferry upriver to Parramatta, but we haven't done that trip. Old Government House at Parramatta (National Trust) is worth a visit and you can combine that with your ferry trip upriver from Sydney to Parramatta.
As you are staying above Central Station you can go by train to Circular Quay to see Sydney Harbour, the Rocks which is where Sydney first started. You can also go by bus (the bus stop is across the road from the hotel) to either the shopping area of Sydney including the Queen Victoria Building or Hyde Park. Lastly after leaving the hotel you can have an easy walk to Paddy's Market (weekend) & continue to Darling Harbour which is approximately a 15/20 minute leisurely walk from the hotel. Hope this helps & will provide you with a good coverage of the city of Sydney over 3 days.
Catch a ferry on the harbour. The best are the Manly Ferry and the Parramatta River Cat. Taronga Zoo is good too and you can catch a ferry there from Circular Quay. You can walk across the harbour bridge for free . The hotel is near Chinatown which also leads down to Darling Harbour. The Sydney Aquarium is worth a visit there.