Hey Rick,
there's a few suggestions in there but quite a few of them are suburan ones and may be a little tricky to get to.
Also depending on what time in january, you may find many of them closed, particularly before Jan 4 due to Christmas and new year holidays.
I've been to elements Bistro at the top of King St in the city recently and it has very good, quite authentic french food at very reasonable prices. It is just a hole in the wall though and may be very warm in January. I didn't know it was BYO, but that is great.
If you want to celebrate and see some fine dining that the city is really known for, the following are my best picks and all are in the city. These are the best of the best:
Tetsuyas. This is arguably australia's best restaurant and if you'd like to go here you should consider booking now. Ten course degustation is $195 and worth every cent. You can also BYO but they have an extensive wine list.
http://www.tetsuyas.com/index.html If you BYO, go for more Pinot and lighter style wines.
Bilsons. You can bring out the big reds here. Classic french cooking done very well. Degustation $165 or $135 or you can go a la carte
http://www.bilsons.com.au/main.htm Sensational wine list but very exy. You can BYO here but they don't really encourage it.
Quay. This has just won every restaurant of the year award in Australia. Four courses $145. They also do a much cheaper lunch which could be worth investigating. Stunning views as they are directly opposite the Opera house. That is provided a cruise ship isn't blocking the view of course. Worth a visit.
http://www.quay.com.au/ If you can only do one, I'd be inclined to go here or tets. Substantial wine list, no BYO. Some bargains, some outragously overpriced.
Becasse. French style again. Not as flashy as the others. Very refined cooking but I was dissappointed the last two times I went here. Mostly as I walked out hungry after spending a small fortune but it is good.
http://www.becasse.com.au/ Overpriced wine list too. There's a range of menus. $130 for degustation or $190 with matched wines or a la carte.
Claudes. One of my personal favourites. This is in Padington so you'd need to get a cab. Should be $10-12 from the city unless the traffic is VERY bad. $135 for three courses or $165 for degustation. Lovely french food in a discreet terrace. It is also BYO but have a wine list too. I would think more Grange has been drunk in this restaruant than any other anywhere. I don't think I've ever been there without seeing a bottle. Of course, quite a few of them were my own.
http://claudes.com.au/about/
Aria has a range of menu options and is right next to the opera house.
http://www.ariarestaurant.com.au/Menus/524/1140/3/0/0/ It and the wine list is quite expensive but it's all good. Excellent mod oz food.
Guillaume at Benelong is also a stunner. This is inside the Opera House so is quite special.
http://www.guillaumeatbennelong.com.au/. Pre theatre special can offer some value or the usual degestation or a la carte. Extensive and expensive wine list. No BYO.
Ottoman Cuisine is not quite the same standard as these but not too far off it. The preceeding restaurants are (or were) all three hats restaurants and I think ottoman is a one hat. (Like michelin stars) $80 degustation or $120 with matched wines or a la carte. They also have an exceptionally good valued wine list that is definitely worth investigating.
http://www.ottomancuisine.com.au/Sydney/Sydney.html
Now for some more down to earth options. For lunch, there are food courts all over the city providing plenty of food for well under $10. These include good ones under Myers, under Centrepoint, a good one in the MLC centre, another good one under Australia Square, a smaller one in the AMP building near circular quay. There are two excellent asian food courts, one in the Hunter connection near Wynyard and one on Pitt St behind and sort of under Woolworths, near Town hall station. You might need to ask someone where this is but it is very good.
Chinatown is also great fun and there's a heap of good restaurants around there. One fun new one is a Japanese one that has touch screen ordering opposite the Entertainment Centre. It's called Wagaya and is at level 1, 78-86 Harbour St, Haymarket. The food is very good and speedy and it's a hoot. It's also busy so you'd need to book but on the day should be fine. Ph 9212 6068. It's also BYO.
For other lunch options, one I'd really recommend is the Glenmore Hotel in the rocks. It's just a pub with pretty normal pub food but they have a roof top area that has fantastic views across the harbour. It's at 96 Cumberland St. The easiest way there is up Argyle st off George st. Just before the tunnel, on the right, there is a set of steps. Go up the steps and it's the pub at the top. More steps to get to the roof but you can have a quenching beer when you get there. You may need to order food downstairs so maybe do that before you go up. You can get a beer from the bar on the roof. On a fine day, this is a magic way to spend the afternoon or at least have a break.
Another fun place is Ivy on George st, near Wynyard. It's only been opened about a year and is a destination in itself. It has numerous bars and restaurant throughout and is a funky place. You can just get bar food or eat in any of the restaurants and there's quite a few including a wine bar. An italian one has just opened up and looks out on to the swimming pool apparently. I haven't tried this one yet. Mid range prices throughout the complex but worth exploring and you won't believe your eyes.
Some other good bars are ECQ at East Circular Quay. You need to go up through the Quay Grand hotel to the bar but then you get to look down at everyone else while they wonder how you got up there. Reasonable drinks prices and bar food. Very good in the afternoons when it's not packed and it's still light. Quay Bar is in front of Customs house at Circular Quay. It's often full of people having after work drinks but it's not bad on a nice day. Young Alfreds is a pizza restaurant doing good pizzas and reasonably drinks on the other side of customs house from Quay Bar. The Argyle is on Argyle St in the rocks and used to be a big wool store. It looks fantastic now and does bar food and drinks. It gets packed with a young crowd on Friday and saturday nights but is nice for lunch. As already mentioned, Opera Bar is great too but gets PACKED on a friday night so go early to get a table or go any other night.
Further afield, Glebe has Glebe Point Diner and Atelier, as already mentioned. Both excellent mid range restaurants doing very good food and BYO. You'll need to get a cab there. Should be around $15. It can be a slightly dodgy area though due to just a couple of out of control youths so get the restaurant to get you a cab to get home and don't wander around.
Newtown also has a million cheap restaurants including thai, japanese and vietnamese. They are all good and they are all cheap and they are pretty well all BYO. Also a couple of good mid range restaurants including Linda's, La Ruscetta and Oscillate Wildly (although you won't get in here - booked out months in advance). It a great suburb to wander around too and is off the tourist route. About a $15 cab fare or get the train to Newtown station.
That lot should keep you occupied for a while. Most of these can be easily walked to from anywhere in the city. And here's a tip, if you're in Sydney for week, but a weekly cityrail pass. A rail pass is about $20 and gets you unlimited train trips around the city circle for a week and a red travelpass for $35 will also get you buses and ferries so you can go to taronga zoo, watsons bay, train out to bondi and buses down to the beach. It won't get you to Manly on the ferry but a Green $43 one will. Then you have one ticket for the whole week and can go anywhere easily and very cheaply. Don't go for the tourist passes as they are overpriced compared to these.
http://www.cityrail.nsw.gov.au/fares/travelpass.jsp