There is riding in and around Sydney – and also between Sydney and Canberra. I can’t vouch for the quality nor its suitability for visiting riders ie bike hire and ease of navigation.
Stromlo is good. It probably isn’t worth the 3+ hours each way trip just to ride there though. Also on a hot day there isn’t a lot of shade.
However as mentioned above there is lots and lots of other good riding around the ACT. Majura Pines are probably the next best and are well signposted. Bruce Ridge is a bit of fun, especially for city workers and if staying at the campsite literally in the trails. East Kowen/Sparrow Hill has around 100km of XC singletrack and some signposting. And there are others.
Depending on work and other commitments I might be able to give a guided tour of Majura, which are my doorstep trails. Likewise I can give you some pointers as to the best trails at Stromlo, not that any of them are bad.
Best bike hire is from Capital Bike Hire:
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Some other useful links:
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http://majurapines.org/
http://sparrowhill.info/
https://selfpropelled.com.au/kowalski-brothers/trail-buddy/
http://flowmountainbike.com/features/must-ride-stromlos-sweetest-six/
http://flowmountainbike.com/features/must-ride-majura-pines-act/
A great resource is the TrailForks website and free phone app. Most of the Canberra trails are covered pretty comprehensively.
http://www.trailforks.com/region/canberra/