If you want good harbour views, it is worth a trip to the cocktail bar at the top of the Shangri La hotel. Lots of people say the bridge climb is pretty cool, though haven't done it yet.
The zoo is pretty good if you are into that kind of thing, and is an easy ferry ride from the city.
Beach? Most tourists head for Bondi or Manly.
Museums - I personally think the powerhouse museum is pretty cool, though the Australian museum is also quite interesting.
You could take a walk through the botanic gardens and sit on Mrs Macquarie's chair, then wander into the nearby art gallery.
The Aquarium, Martime Museum, Star City Casino are all walking distance from the city.
sorry - riggling child on my lap - will try to add a bit more later...
edit - ok child in bed. You might also want to check out centrepoint tower.
Food places - King Street Wharf has pretty good eating spots and bars, though it can be a tad pricy (if your work is paying, I say take advantage...).
If you are after night life, perhaps you need to ask someone else - I'm a little disconnected from that scene, though Oxford Street and Kings Cross (as Latch mentioned) will usually have some midweek action.
You could also visit Luna Park (just across the harbour bridge)
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