Parking is free, secure and under cover everywhere in the Melbourne centre compound. so no worries there. If you're from out of town and want to fly home, you can park your car there for free and not have to worry about it.
If you're on a tower course, you'll have to spend 4 days at the BoM training school in Broadmeadows. I and one of my course-mates had our cars broken into during the course and getting Airservices to pay for it, despite what's in clause 21 (or is it 23) of the the agreement is a bit of a problem.