I'm no too comfortable with miles, so I converted it to Km: it's around 281 km.
I think that the question is asking for Sidney, because around 240 km north east (we can't go too far east or we would end up in the ocean!) from Canberra is Sidney, and it's the only city in the area. it's 240 km in a straight line, but it would be around 280 if we take into account territorial obstacles!