Canberra is the most bizarre city I have ever been to, it has everything you would expect a city to have except people and, naturally being Australia, public transport. Their natural history museum is fascinating and the Botanical gardens are full of Kangaroos, there is the most enormous park in the middle of the city and you can walk up there to a tower on top of the hill which gives you great views of the city and surrounding area.
Sadly though, some of the best things to do in Canberra are actually outside the city, for me at least visiting the NASA satellite tracking station would have been a great experience but I had no way of getting there.
Rosko recommends: Have a car if you go to Canberra, all the best things to do are outside the city, and the public transport is non-existent.