The
Polish Festival is being held on the first weekend of the tournament (17th-18th). It's not what it once was, as the neighbourhood really isn't overly Polish even compared to 20-30 years ago, but there are a few good Polish restaurants left, plus the street vendors, live music, traditional dance groups, etc. While it's not one of Toronto's premier festivals anymore, it will give you a taste of the ethnic festivities that happen year-around in this city. To get there, take the Bloor-Danforth (Green) subway line to Dundas West station and then it's about a ten-minute walk directly south (there's a fork in the road where Dundas breaks towards the east, continue going south/to the right, on Roncesvalles). The neighbourhood along Dundas isn't the best but it's not unsafe either.
The
Ukrainian Festival is also happening the same weekend (16th-19th). Never made sense to me why they have it on the same weekend. I've never been, but it could also be an option. To get there, go three stops further on the Bloor-Danforth line to Runneymede Station. Polish pierogies are better though. Just saying.
Other than that, lots of good suggestions in this thread. The ROM is probably Canada's top museum. The Aga Khan Museum at Eglinton and Don Mills (it's a bit of a trek from Downtown and you'll need to take a cab... the Eglinton subway line won't open until 2020) is an Islamic art and antiques museum and one of the top museums of its kind outside of the Middle East. St. Lawrence Market and Distillery District is worth checking out. And if you can, make the trek out to Niagara Falls. The city has it's own mini-Vegas vibe going, it has obviously the Falls themselves, and if your into wine, the surrounding area offers some wonderful wine tours.