Good news.
I see Renee has already made some suggestions and I have no doubt that Media Man will be reminding you all to visit Bondi (I used to live there as well) 
.
I thought I’d share some personal pointers of places you should consider visiting in our beautiful city.
Food
Having travelled extensively and lived on four continents, Sydney in my opinion has some of the best food in the world, at pretty reasonable prices. Although you can have any type of food imaginable, and blow your budget if you wanted to, you will find an incredible variety of seafood and Asian food. We have a lot of Asian Sydney siders and they have brought all the wonderful flavors with them.
Some of the best restaurants I have recently dined at are:
Flying Fish in Darling Harbour (Sri Lankan). Awesome (I MEAN AWESOME) prawn (shrimp) curry.
Long Grain – Darling Harbour – adventurous Thai Fusion – unbelievable flavors.
Icebergs overlooking Bondi Beach- See, be seen, have cocktails, and eat some interesting food. An Icon.
More beach side dining – At Balmoral Beach (one of the most picturesque beaches in the world) – Bathers Pavilion. Excellent Cafe faire and an even better restaurant with an impressive wine list. Stroll along the promenade before / after your meal.
Azuma – Japanese – downtown. Award winning Japanese. Pretty traditional.
See a pattern here? I can go on and on. If you don’t see anything you fancy here, I’m sure you’ll find it. We have a “Hat” system by which the best restaurants are graded. Current restaurants with Hats (1, 2 or 3):
xxxhttp://www.smh.com.au/news/good-living/2007-winners/2006/09/04/1157222070830.html
Coffee
Yes we are coffee snobs. Starbucks has never made it here. The average Aussie has about 400 coffees a day and most are quite particular how they like it. Serve bad coffee and your shop won’t survive in Sydney. Most coffee shops have formally trained Baristas. If you can walk 50 feet and not pass a coffee shop, I’d be surprised.
Shopping
I would recommend a walk through the Victorian Galleries for an interesting shopping experience. The old mall and adjoining alleys throw up something interesting on every visit.
Renee mentioned the Rocks market which will be very close to the Hotel. Real touristy but good for all the gifts etc
Cheap shopping at various tax free malls. Best is in Haymarket where you’ll also find the Paddy markets.
Other than that I’m allergic to shopping so not a good guide I’m afraid.
The good news is that if you come here with one of the big three currencies you are coining it – Aussie $ is the weakest in years (e.g. In July it was even with the US $ and now you get almost 1.5 Aussie $ for your George Bush Pesos) :tongue:.
Walks
We love walking so if i’s your thing please ask me. Assuming you are all staying in the Rocks area, there are two equally interesting walks from there. The first is across the Harbour bridge (not the famous walk to the top), but on the pedestrian walk way. It’s mostly flat but for stairs on either end. Spectacular views of the harbour. About 45 minutes from the Rocks to the other end. You get to Milsons point where I suggest s swim in the famous North Sydney Olympic pool and a coffee at one of the coffee shops in Milsons Point. Concierge should have a map that includes this area.
The second walk is a bit longer but very much worth your while. From the Rocks you can walk via the Opera House, and enter the Botanical Gardens. Beautiful Gardens with stunning water views.
If you are staying on for a while I recommend a Ferry Ride to Manly and a walk from Manly to The Spit – stunning scenery and you can take the bus back to the city).
Finally, one of the most spectacular walks you will ever see is the Bondi to Coogee walk along the ocean board. It’s spectacular with views that go on forever. I highly recommend this. Every visitor I have taken there has asked me to go back. Great Coffee(haha) in Bronte Beach. It’s about 45 minutes to one hour to walk there (one set of hectic stairs – rest is flat.)
I can recommend loads more walks so let me know if you are a walker.
Water
We have water. Lots of it. We go in it, on it and under it. A lot of the time. Sydney has been accused of neglecting the arts because it thinks the ocean offers enough (which to some extent is true). I’ll recommend places that are easily accessible by public transport (there are better options if you have a car).
Best for body surfing – Bondi Beach and Manly Beach North Steyne
Best for calm waters – Read Loaf pool or Historical Greenwich Baths – both a bus ride from the city – 5 – 10 minutes (there are better options but more complicated to get to).
There are various options for Sea Kyaking. If it’s your thing, let me know – there’s a good tour or two you can go on.
Ferries
We have Ferries that connect most major parts of the city. Definitely take the Ferry to Manly. Great walk along the promenade. My favorite Italian Deli is there – Three Olives. And yes, they make a good coffee :wink-wink
If again you have more time, I highly recommend a Ferry ride up the Paramatta River. Grab lunch in Paramatta.
All the Ferries leave from Circular Quay – 5 minutes from your hotel.
Another great Ferry Ride goes to Watsons Bay. It’s only 20 minutes. Either go to for lunch (excellent Seafood) at Doyles or Grab some Fish And Chips and site along the promenade. There’s a great beer garden here as well with good food.
Finally if you like the Zoo, ours is supposed to be one of the best in the world I’m told. Take the Zoo ferry from Circular Quay. You can check out all the Aussie animals, pet a Koala and do some Mixed Martial Arts wit ha Kangaroo (kidding 
Cabs
Easily accessible and reasonable.
Maps
Use google maps, although the local map site is http://www.whereis.com.au – sometimes more accurate.
That’s all I have time for now. If you want advice post it here. If I can’t answer, I’m sure one of my fellow Sydneysiders will.
Oh, BRING A HAT AND SUN SCREEN. Trust me.