"...Canberra), and find it's actually more car-centric than where I lived in Sydney, which is a shame."I don't live in Canberra but from my many visits there my experience is that it's harder to go from A to B there than in Sydney (and Sydney is no shining light when it comes to getting about).
That said, Burley Griffin's planning and layout for Canberra is a delight when compared to Sydney's dogleg-like haphazardness. Thus, it's likely that Canberra's openness makes getting about more difficult but there are probably other factors that locals are more aware of than I am.
I suppose I am sensitive to issue because for a period I lived and worked in Europe and my main base there was Vienna. Getting around Vienna is simply a dream when compared to either Sydney or Canberra and I put this down to the way the Straßenbahn (tram) and U-Bahn transport networks work in that they are tightly coupled together in ways that facilitate the easy movement of people.
Somehow, despite the fact that Vienna is a very old city with for the most part very narrow streets, the Viennese have installed a transport network that works extraordinarily well in the circumstances. (I would concede however the city had one advantage in that the old city walls were demolished in the last quarter of the 19th Century which made way for a ring road (Ringstraße) which greatly aids public transport.)
But the Ringstraße was only part of the solution. The main issue, not only in Vienna but in many other European cities is the attitude of city planners. There, much more attention is focused on public transport and it seems this attitude has prevailed for many decades unlike the haphazard planning in Sydney (it's always been a political football here).
Some say we can't plan like the Europeans do as we've not the population density and no doubt that's partially true but for some reason their attitude to planning is much more utilitarian and long-term than here. I think this is the key difference.
Edit: to be fair I must add that in recent years Sydney's public transport has improved significantly even within confines of its existing infrastructure. Whilst some new rail routes/infrastructure have been added what has noticeably improved is the service, buses and trains are reasonably plentiful and importantly are usually on time. This makes public transport much more attractive.