My favorite is the Bateau de Nuit, but you kind of have to like dive bars and heavy metal for that one. Some others: Le Projet (my 2nd favorite and good for dinner), La Barberie (relaxed with a nice outdoor area), Brasserie Artisanale La Souche, Ninkasi St-Jean, Brasserie L'Inox (there's also a Les 3 Brasseurs right across the street which is OK), Le Sacrement, Griendel Brasserie Artisanale, Noctem Artisans Brasseurs, Le Korrigane
Saint-Alexandre have a decent cellar of bottles with lots of Belgians, a little expensive though, but the service is good and the place neat.
As a tourist to Quebec City I found the pub Sainte-Alexandre to be excruciatingly touristy (and of course it is, with all of those tourist in that area just off of their cruise ships - what else could it be?!). It reminded me of one of sooooo many fake "English" pubs that I've been to that could have been from any part of the world (Germany, Italy, Spain, USA, China, Japan, etc.); and worst of all, they didn't really have any true local beers on tap, only the bigger players. The only thing worse in my opinion would be the Pub Saint-Patrick, but at least there you might get to sit on the deck if the weather is nice! I'm only semi-kidding about that, but if you're visiting somewhere you should try to learn about what's there - what's really there - and not just visit mock-ups of bars and restaurants from other parts of the world. Just my two cents. Hmmm... and thinking about "cookie-cutter places", maybe TheDoctor is right about Les 3 Brasseurs! I've been to about 5 of them! Still, I'd rather go there and get a beer that I can only get there than something that I could find almost anywhere.
I am obviously not a fan of L3B but you are absolutely right. And, chain or not, the beer all depends on the brewer at the particular location. I have admittedly had good beer at their bars. They even go so far as to have chain-wide brewing competitions which is kind of cool. And each location has a signature beer that is only brewed there. However, if given a choice between Unibroue and L3B I'd choose Unibroue. The 3 brasseurs stout is usually pretty solid though I find. Next time you're up this way, drop me a line.