Hello Claire and welcome!
All the tips to find a place in Toronto are on the forum but unfortunately in French... that's why I moved your message to this "english speaking board".
To find your apartment you should have a look on this website, the best in your case I think:
MyHood.ca -> perfect for you as you can search in a specific area of the town, then scroll down on the map to find only the apartments available next to UoT: easy!
Other than that, for the most famous ones, you can also try
ViewIt.ca,
CragList and
Google.
The best would also be to walk around the neighborhood you want and check for the "for rent" signs in the streets or ask directly in the buildings' management.
Hope that will help!
And by the way, "Claire" sounds French: where are you from? What are you doing in Toronto?