It really depends on what you want, but here are a couple of suggestions:
Laurie Raphaël (117 Dalhousie, Old City)
L'Initiale (54 St-Pierre)
Le Café du Clocher penché (203 St-Joseph est)
Québec institution: Le Continental, very near le Chateau Frontenac. Go for the duck flambé or some of their other classics.
Something less upscale but very pleasing is Le moine échanson on St-Jean, which is a bit of a wine bistro. It has received very positive reviews over the last year.
Being a student, I have only had the chance to go to Le Continental and Le moine échanson. LR and Initiale are considered five stars restaurants around here and Daniel Véniza from LR is a bit of a 'celebrity chef' in the province.
Hope that helps!