Star City Casino overlooks the neighbouring Pyrmont Bay, and is only a short walk, or a couple of stops further on the light rail, from Darling Harbour. It has everything you would expect from a casino, tables, gambling machines, buffet restaurants and sports bars, as well as more than just a little kitsch.
The Powerhouse Museum is close to the Entertainment Centre, and is immediately adjacent to Darling Harbour in Ultimo. There are signs directing you there from all around the precinct. It isn't quite a science museum, and not quite a natural history museum, but its not drab or boring. There are interesting parts of Sydney's modern heritage, as well as lots of buttons to press, and plenty of how things work displays.
The Sydney Fish Markets are also close by. again just a couple of stops further on the light rail, or a 10 minute walk from Harbourside. It is a good spot for lunch, or to buy some shrimp prawns for the barbecue.