Well, you could go down the classic high-end french/terroir route and aim for the St-Amour (as suggested), the Panache, the Toast! or others. However, you mentioned steak and it's not something that will typically be on their menu and since they are heavily inspired by local ingredients you will probably see more game meat then actual beef.
There's really only three upper-class steak houses in Quebec City: The Charbon near the Old Port, La Bete on Laurier Blvd. and le Befroi on Place d'Youville in Old Quebec. I've tried the first two and I would recommend the Charbon. Both are nice posh places, but the Charbon's location is better (close to Old Port and Old Quebec) and the service and food is more "mature"... La Bete is relatively new and it shows in some spots. I've heard good things about Le Befroi but since I haven't been there personally, I can't recommend it. In any event, all three offer what you expect from a high-end steak house: Good portions, great wine lists, dry-aged cuts, etc.
Not sure if an actual steakhouse is your idea of "romantic", depends on if the atmosphere or the food is more important to you and your partner.