Lake Gillawana used to be nice for a bicycle ride.
Rookwood cemetery has kilometres of winding roads, and fantastic headstones and mausoleums to inspect. With slow traffic, it's a great place for beginners to ride around.
If there are people working on some of the old mausoleums, they are usually happy to let you have a look around.
Nice canals and old water features - it was designed by the same guy who laid out the Botanical Gardens. Originally had a railway connection and four stations.
Lots of famous people's graves to see.
The Crematorium is the oldest operating one in Australia - was originally coal fired; and even has ashes of Boer War veterans interred in the older walls The columbarium worth inspecting.
There are people who keep bees there, because all the flowers and trees make great honey.