Parking in UNSW is really hard to come by. I find that the streets over near matthews building usually has some empty spots however I gave up on driving to uni. Parking isn't that bad though if you are prepared to walk 10-15 min (or longer).
Things to watch out for though are those pesky 1 or 2 hour parking limit spots which seem to pop out randomly on the streets around the uni. Also, dont park in Mc Donalds, they chalk tyres and have a strict parking limit for customers only. Finally, watch out for garbage day. When there are bins on the street, dont park in front of them.. you could land yourself in quite a bit of trouble.