Parking in downtown Toronto is not the best for cars and definitely not cheap. Most lots are underground or in towers that have height limits of about 2 metres (6-7 feet) and a lot are designed for smaller vehicles, some have width restrictions as well.
Your best chance would be at Exhibition Place
Exhibition Place Parking. This will be further complicated by the PanAm Games July 10 -26 ParaPanAm Games Aug 7 - 15 and Finally the CNE (Canadian National Exhibition) Aug 21 - Sept 7.
Good Luck Ken