Years ago, Gonzaga turned a couple of rows of old student and theme houses into a centrally-located parking lot. What the University lost in soul, it made up for in convenient parking. The dorms and the campus apartments also have some parking around them, and you can get a pass for one of these sections if you're proactive. The majority of on-campus students doesn't have a car, so competition for specific lots isn't too intense. Still, the "parking in one lot only" system can be a hassle, and you will be ticketed if you try to park in a differently coded lot.
Off-campus parking is only mildly inconvenient—one can almost always find a spot within two blocks of your intended destination. Off-campus parking is also free, so it's hard to complain too much about it. Still, you should hone your parallel-parking and block-circling skills to truly flourish in this semi-competitive environment. In nasty weather, any walk at all can seem like a colossal pain, but that doesn't change the objective fact that free parking three blocks from your classroom is a pretty great deal. Both on and off campus, be wary of breaking rules. The Man is out in full force, and he is looking to screw you over.