I hate parking at ANU. I used to have great satisfaction when I came in to study on the weekends and could park in the car park opposite union court for free. I don't know why but it just made me happy.
I believe (but I don't know) that you can buy a car spot or something with one of the residential halls. It costs more but think they only have a certain number so you'll always get parking.
I hate to admit it, but honestly 90% of Canberra could catch a bus to ANU. Sure it would take longer and be annoying but Canberra is pretty small. So maybe its not a bad thing that they have less parking - they are encouraging people to use alternative means.
Saying that I used to drive everyday and I lived pretty close. That was partly because I have so much stuff and partly because I needed to go to Belconnen after, so its kinda on the way. I used to park across it Turner. Its really not that far from Union Court and if you drive around there is always parking, although sometimes you have to take the not so ideal ones. Basically there is two hour parking, three hour parking and after 11am parking. So you are going to have to move your car once during the day. It wasn't a huge deal for me, I over stayed by a couple of hours multiple times and never got a ticket.
That worked for me, you might not want to do it but I saw it as the best option. Giving less money to stupid ANU car park services and also costing me less.