For many, L'anecdote has the best burgers in Montreal. Aside from the classic beef, they also serve veal, dear and boar meat burgers. I believe that I remember a vegetarian burger too. The fries are very acceptable.
The alcohol selection is interesting although I always end up sharing the same bottle of wine, which is (of course) twice the price than the SAQ's, but still affordable: around 20$ for a bottle in a restaurant is a pretty good deal.