Cycling Path from Tuggeranong to Fyshwick

[Slartibartfast]

I'm new to Canberra and currently live in Greenway (Tuggeranong) and find my self needing to head to either Kingston or Fyshwick every so often. As it is though, I have been unable to find a suitable path to ride, so invariably end up driving the car. Is there a good way to get from the Southern reaches to the Eastern suburbs on a bicycle?

With Canberra having generally excellent cycle ways I've been able to ride to most places I should ever need, but the only ways from South to East I can find seem to be either following the Monaro Highway or taking the cycle way into to Woden then Hindmarsh Drive across, neither of which are at all appealing. Using Google maps I have been able to plot a course from Tuggeranong, up to the southern side of lake Burley Griffen then, following the southern shore line, head east but it sure seems a convoluted way to get there:
Google Maps Link

Is there a better way?

[Noviss]

A more direct way would be to jump on the on road lane at Yarra Glenn/Adelaide Avenue and follow it all the way to Flynn Drive which cuts out some of the scenic detour via Yarralumla.

Hindmarsh Drive is the most direct route but I get why you would avoid it.

Google maps is good but search ACT cycle paths and you will be able to download an ACT Govt map which shows on and off road paths. It is better but hasn't been updated for a couple of years.

[Howzat]

What Noviss says, unless traffic is heavy, in which case the bike path may be preferable. When you get to Kingston, take Eastlake Parade, rather than sticking next to the lake.