If you are fit, I would get out and walk. Darling Harbour is nice, but no one big attraction, the Chinese gardens are attractive, but probably no need to visit the aquarium or the wildlife park. You could actually visit the Chinese gardens and then stroll from their along Darling Harbour to Barangaroo, and onwards to Walsh Bay under the harbour bridge, and all round circular quay, through the botanic gardens and finishing at Mrs Macquaries chair. That's a good 8kms. I also like a stroll around Bradley's Head by Taronga on the North side, or on the South side, at Vaucluse, around either Nielson Park or South Head. The views of the harbour are beautiful from these places. The first is probably easiest by public transport, take the ferry to Taronga and then just stroll. If you want activities you can walk/climb up to the mid-point on the bridge, courtesy of Bridge climb, that's very expensive but of course the views are stunning. Also you should check out some aboriginal art in the Art Gallery of NSW. More walking, but the Coogee to Bondi walk along the ocean front is popular, but not completely unmissable. It gives a different perspective of the city.
Make sure you get ice cream from Gelato Messina, there are several branches, at least once. Seek it out over alternative brands, you won't regret it. We also like to get a 'hug in a mug' at Max Brenner, it's hot chocolate, and Emporers puffs from the window in China town. There are lots of restaurants with views in circular quay, but you need to check the cruise ship schedule as the boats can entirely block the view! Food with a view is not always great/good value unless you are eat in either Aria or Quay, which will cost you a fortune. Both Sushi and Thai food is almost always much better in Australia than the UK. There is a little area they call Thai town near central station, with a wealth of Thai restaurants. We have a habit of eating at Sushi bar Makoto, but other places are probably just as good for sushi. Sydney prices for everything are high unfortunately.