No idea about Quebec City but here are my recs for Montreal in no particular ranking:
Japanese:
-Park restaurant, in Westmount
-Nozy, around Atwater Market
-Kazu, downtown on Sainte Catherine Street
-Kampai Garden, downtown on Ste Catherine also
Typical French Canadian meat heavy:
-Chalet BBQ, in NDG (best rotisserie chicken in the city)
-Au Pied de Cochon, in Griffintown
-Joe Beef, also in Griffintown
-Garde Manger, in Old Montreal
-Grinder, in Griffintown
Smoked Meat:
-Schwartz's Deli, on St Laurent Blvd (don't even waste your time eating any other smoked meat)
Legit High end steakhouses:
-La Queue de Cheval, downtown on de la Montagne
-Moishe's, on St Laurent Blvd
-Gibby's, in the old Port
-Lavanderia, in Westmount next door to Park restaurant
Vietnamese:
-Pho Bang New York, in Chinatown south of Rene Levesque Blvd (best Vietnamese soup in the city imo)
Chinese/Dim Sum/Sezchuan:
-Restaurant VIP (open til 4 am) in Chinatown
-Cuisine Sezchuan, downtown at Guy/Sherbrooke streets
-Le Crystal Chinoi, in Chinatown
Greek:
-Tripolis, in Parc Extension
-Parthanon, in Snowdon area
Pizza:
-B&M pizza, couple locations
-Pizzeria Elio's, in Ville ray/Petite Patrie
-Chez Dany's, downtown on de la montagne
French Bistro type places:
-Aux Poi Penché (excellent raw bar), downtown
-Chez Alexandre, downtown
-Méchant Boeuf (excellent raw bar), in Old Montreal
-L'entrecote Saint Jacques (fixed menu of soups, salad, ribeye steak and desert, love this joint), downtown on Peel Street
Portuguese:
-Ferreira (known for their seafood), downtown
-Romado's (best Portuguese rotisserie) in the plateau off St Laurent Blvd
Hot Dogs, Poutine and Burgers:
-Any Lafleur's location is a legit Poutine
-Montreal Pool Room, a classc late night poutine hot dog and hooker spot, on St Laurent south of Chinatown
-Dilallo burger, on St Joseph near Joe Beef