There’s a Lonely Planet guide to biking in Australia that sets out some suggested rides (
http://www.amazon.com/Lonely-Planet-Cycling-Australia-Guides/dp/1864501669/ref=sr_1_2?ie=UTF8&s=books&qid=1233706802&sr=1-2), if you have time to get hold of it (and can afford its startlingly high price). I don’t know if you’re planning to camp or are looking for accommodation on the road; you will probably find tourist campsites in most places.
1. You can go north to Newcastle and the Hunter Valley, a very well-known wine-making area and popular tourist area. Great food, great wine, pretty easy cycling. Easy(ish) to get out of Sydney along the Old Prince’s Highway and side roads through national parks.
2. You can go west from Sydney to the Blue Mountains. You can either take the train to Katoomba or Lithgow, an easy hour or so that will avoid a steep climb, or take Bell’s Line of Road to Katoomba. After that, go to places like Bathurst, Sofala, Kandos, Rylstone, Mudgee (great wine and food, excellent cycling), Gulgong. Stunning scenery. I recently did a supported tour in this area, loved it and would love to go back to do it in a more leisurely way.
3. You can go south-west through the Southern Highlands through Bowral, Moss Vale, Mittagong and Goulburn to Canberra – great scenery, wine and food; perhaps use Canberra or environs as a base for some day trips before returning – perhaps along the South Coast.
4. You can go south to Wollongong and beyond along the coast – stunning scenery and food. Going through the Royal National Park is a great start – unequalled scenery along the coast road. A short train trip will get you to the start, though the suburban riding is not too agonising. Possibly a bit tricky after Wollongong as the main road is a narrow heavily used highway – seeking out side roads might be worthwhile but will take some planning and navigation.
You can combine options 2 and 3 or 4 and 3. Good luck; let me know if I can help in other ways.