Sydney Olympic park has 35 km of good safe trails with lots of scenery and some really interesting places to discover. All the bike trails are double lane.
To get to the park by car, there are car parks everywhere. Only on sunny weekends after 11am will you have to hunt for a spot.
Better still arrive by train and the best station is Rhodes as it puts you in a great spot for riding. Olympic Park station is fine too and both have lifts for your bike. As usual with bikes on trains, avoid peak hour, go early if you can and Sunday is the easiest.
You can put your bike on the ferry and arrive at Woo-la-ra Quay. That would be cool but watch for busy times as you could be refused.