There are many interesting locations to explore in Toronto on a rainy day. In fact, if the weather is not co-operating for more than one day there are more than enough enticing diversions in the city:

Note: these attractions are linked to their TripAdvisor listings. From there you can access the attraction's website for more information.

Museums and Other Attractions 

University of Toronto Art Centre

Art Gallery of Ontario

Gardiner Museum of Ceramic Art 

Royal Ontario Museum

Bata Shoe Museum

Hockey Hall of Fame

Casa Loma

CN Tower

Ontario Science Center

St. Lawrence Market

Popular Malls

Eaton Centre 

Sherway Gardens

Yorkdale Shopping Centre

Square One Shopping Centre

Upscale Malls

Hazelton Lanes Shopping Centre

Bayview Village Shopping Centre 

Queens Quay Terminal

Toronto Antiques on King

A few other ideas:

Glenn Gould Studio

Academy of Spherical Arts

Colossus Movie Theatre (Gigantic movie theatre ..looks like a flying saucer)

Chapters - World's Biggest Bookstore

The Hollywood Canteen