Three days in Sydney Eh? - Well depending on your taste, there are heaps of things to do. Now how you go about things in January is up for some question. If you come from a hot state - no problem but if you come from a cold climate January can get a bit uncomfortable, as it is right in the middle of summer, so lots of heat can be expected and possible rain (warm rain). However New South Wales has a much dryer heat than we get up here in Queensland so it is not so oppressive, but plan take things at an easy pace.
Naturally the Opera House is a must, it is not really that impressive but at least you can say that you did it but if you elect for the full tour be prepared for a lot of walking. If you have lots of loot you can book in for dinner at the Bennalong Restaurant. Food is passable (expensive) but the view is great.
Captain Cook Cruises run super harbour tours both day and evening, the day tours give you the sights but a dinner cruise shows the city off to best advantage, Sydney really does shine at night.
If you want to get out of the city you could take a tour to the Blue Mountains (full day). Once there do not expect a huge tourist infrastructure, you go mainly for the views of the Three Sisters and the landscape which goes off into infinity. This is a long tour but it does show off the suburbs and how they fade out to the bush.
There are Good Hunter Valley Wine tours which depart daily, will cost you around US$45. For around US$50 you can combine a harbour cruise with Featherdale wild life park - that is if you want to see some cute and not so cute creatures.
Darling Harbour is a good place to spend a few hours. This used to be the old Pyrmont Wharves area and I dispatched many a cruise ship from here many moons ago) - now it is a very plush and vibrant place to go and view the inner harbour, do some shopping, have a meal and a few cool drinks.
The Rocks area behind the Circular Quay wharves is a good place to go and get a bit of the history feel of the city, (Sydney has a cruel and violent history) even though it has now gone touristy.
My suggestion. Day one - do Either Blue Mountains - Hunter Valley, then come back to the city and dine in one of the many restaurants that hug the harbour.(Or a show at the Opera House)
Day two - Do the Opera House in the morning - then to The Rocks - then over to Darling Harbour. In the evening do a dinner cruise with Captain Cook (John Cadman Dinner Cruise) approx US$50 - After that -well there are heaps of nice bars and things to while away the rest of the night.
However - having said all that - none of it may suit your taste. Not to worry Sydney is the sort of city where you can just wander and find things to do. - Even go to Taronga Park Zoo which is interesting and only a ferry ride away (great harbour views from the zoo)
The Intercontinental Hotel is OK and does have a desk where you can get any of the above arranged.
Hope this is of some help