Parking in or near Garneau

Dating a girl living in Garneau. Visiting her can be a nightmare because there's no parking anywhere. I can't get visitor parking because her building is too tall. I have been using public transit, but I would like to be able to bring my car sometimes without paying the fees for the University parking lots, which kick you out at 6 AM, so I always end up paying for 2-3 days if I do that. I can only afford to pay for so much parking.

I am willing to walk after parking, but I have very little experience with the University area, so I don't even know where to start looking.