Hi Ellen
There are no doubt lots of options around Sydney and I'm not a local so others will have better ideas. However here is a route I used when doing a tour of northern NSW 10 years ago
http://www.bikely.com/maps/bike-path/Ma ... Palm-Beach
http://www.bikely.com/maps/bike-path/Pa ... -Macquarie
I left Sydney on the ferry to Manly, cycled along the northern beach suburbs to Palm Beach, then took a ferry from Palm Beach to Patonga Beach and rode on from there. First night's camp was at Umina Beach. They had plenty of on-site vans. This route took me out of Sydney with very little traffic stress. The only area wherre I had some busy traffic was from Umina Beach to Terrigal. From here on I cycled almost entirely on quiet country roads through small towns. There is one section of gravel road at Monkerai north of Dungog, but despite local misgivings it was lovely. There was another gravel road climb to the Comboyne Plateau. It was steep. If you get this far allow a good 4 hours for the 25-30 kms from Wingham to Comboyne! It took me 10 days to get to Port Macquarie, with one rest day at Gloucester, and another at Laurieton. You could probably cut off after 7 days at Taree where you could catch the north coast train.
Beware, NSW trains only carry
two bikes, packed into a box

and you must book them in advance. For the best bike/rail touring in Australia come down to Victoria

Riding bikes in traffic - what seems dangerous is usually safe; what seems safe is often more dangerous.