You can drive here and park easily, but it's really not a big deal to get the bus from the Mont Royal Metro, and there are so many other tourists doing the same you won;t get lost. Another advantage of this method is that you can go back down into the Plateau to stroll or dine after you're done on the Mountain and not worry about parking.
The Viewpoint at the Chateau is extraordinary, one of the rare must-dos that really is. the Chateau itself is huge and impressive, there are vending machines and a small gift shop so bring food if you want to do a proper picnic.
From here you can stroll down to Lac du Castors (fenced off for construction as of this writing) and the large children's play area nearby.