JosephC said "The city has been working on a plan to redesign the library in its current building. I highly doubt it will be moved out of downtown given all the work that has gone into that and given that its my understanding the city owns the building the library is currently in. "
Also, accessibility. You can get to the downtown location on a single bus fare from most places in the city. Anywhere else would require 2+ fares depending on where you're coming from. Seeing how the library is supposed to be accessible by all income brackets, it makes sense to keep it in the area where it is.
There is already a suburban option for the library - at the Shoppers Mall. If you're going to drive to the west end, you can just as easily drive to the south end. Sure, ideally we would have a branch in every quadrant, but that's probably not feasible until we hit 100,000-ish people.
Same thing with Giant Tiger - while the store is small, the location is more accessible for those not having cars. Moving it means zero places to buy basic groceries between 9th St and 34th St. That's a long, long walk just for the chance to buy groceries.