Restaurants: The Very Nice - Aqua Luna in north sydney-not far from Luna Park (old fun park on prime land) or Rockpool in the Rocks area or The W Hotel in Woolloomoolloo. Sunday brunch, go to Panarama in Bondi for a yummy breakie.
For fun and a good meat pie, cant go past Harry's Cafe'd'Wheels, in Woolloomooloo, near Garden Island naval base - get the pie, peas and mash - great night time atmosphere and its just down from The W hotel. The Flying Fish at Pyrmont (near darling harbour) and even the sydney fish markets offers good meals or just get some oysters at the growers co-op and cooked prawns and sit by the water having lunch. a bit out of sydney - Noahs at Palm Beach - sell the house to pay for it but the view is worth it. oh, otherwise get a sea plane and fly to berowa waters (or Noahs) for lunch and back.
Fun things to do: Sydney Harbour Bridge climb, even the locals do this - its fun.
Manly Aquarium does shark dives for a bit of cheessy fun. if youre here in summer - try to catch a game of cricket just for the fun of it. on the weekends, go to The Rocks markets and the Lord Nelson pub is good for good ale and food any time.
If you are coming in January go to a open theatre night (catch a movie at botanical gardens overlooking harbour) or taronga zoo night visit (also prime land location).
Sydney Observatory night tour also.
If just want to hang out by a ocean pool and relax - Coogee baths (near Gordons Bay) and yes, hit the pub up the road afterwards.
and another big yes to catching some ferries around the harbour to see the sights for a fraction of the cost. take a packed lunch and enjoy or do a kayaking harbour tour.
do a day tour of blue mountains - i think the company is called Tread Lightly tours and they offer small groups to areas the bigger companys dont go to.
take advantage of our sydney olympic facilities. white water rafting at penrith or go to the main stadium for archery, swimming, bike riding ect - all fun stuff you might not do at home.
If your diving, put kurnell in Sutherland Shire on your list for weddy sea dragons or Magic Point at Maroubra for grey nurse sharks.
if i had family coming - these are some of the things i would be thinking off so hope its some help and youre welcome to PM me if you have any questions.
cheers