I've had trouble finding free internet. Most of the hotels I've stayed at had free internet so your best bet is probably to hop into one of the restaurants below the hotels (Pretty much all of them have one) and set up there.
All of the Safeway Grocery Stores provide free wifi. Have a seat at the Starbucks and surf for free. The internet is provided by Safeway, so you don't need to purchase anything from Starbucks to get online for free.
Downtown you can find open wireless at the Forks (in the coffee bar in the Johnston Terminal building), at the Twist café on Graham at Edmonton, and at Spin City laundry, on Edmonton between Broadway and Assiniboine.