This is exciting. Without knowing how long you're in Toronto it's hard to give other suggestions, but I can try. Shoot me a PM and happy to help with anything specific - restaurants, shopping, bla bla.
But like piper1 said, go to a jays game. If its in August its going to be hot as f and if the dome is open it will be awesome. Fun (little known) fact: you can bring whatever food you want into the rogers centre - homemade sandwiches, a sub from across the street, a whole pizza. Anything goes food wise but drinks are obviously a big no-no.
As far as the Hockey Hall of Fame goes, it's kind of you see what you see. Nothing really hidden or special. They used to host these 'industry nights' for lack of a better phrase where essentially the whole hockey hall of fame turned into a bit of a bar scene - a few bars scattered around, some guy playing country music in the middle of it, etc. I went a few times and had a blast, but I have not heard about them for a while.
