Street parking is free. Make sure YOU READ THE SIGNS - because they tend to switch from 1hr/2hr zones to no-time-limit zones and it's so easy to get caught in "that" spot .. why was it vacant? $68 later you'll find out.
Depending on where your classes are, there's plenty of parking around UNSW. If you don't mind the walk up the University Walk you can park on the other side of Anzac Pde. Get there well before 9am if you want to get a decent spot though. If you are in Engineering/Commerce (like me!) I like to park on Barker St/Willis St which is on the Maccas side (college side) of UNSW - make sure you can reverse park on hills, and don't worry when people get pissed off cause you find a spot. Just take it
If you're on the other side of the campus mostly you can try to find a spot on High St but I don't like your chances.
And finally upper campus people can find parking on the highest part of Barker St, towards Randwick. It's usually easier to find parking here in the mornings for some reason, but it's a bit of a walk at the end of the day (up all those hills..)
I'm lazy so I don't like parking past Middle St - anything longer is a HIKE. You could also pay for a permit, or park in the parking station (it's $8 all day IIRC, and you can park on the upper levels) which has an entry on Barker St. There's also one up the top of campus if that's closer to your classes.