I went to Auberge Michel Doyon last week with 4 friends, and we had a great time. The place is clean and the beds are very comfortable, but the most important thing is that the service was amazing. Serge guided us in Quebec City and showed us many great places to go to, and the staff was very friendly (they even gave us breakfast 4 hours past the time!). They also have everything you need (free parking, TV, internet, etc.). The only problem is that the Auberge is not downtown, but it is not that far either (around 20 minute walk), and on a bus line.

Well recommended if you're looking for a reasonably priced place. I needed a room with private bath and couldn't book one with the hostel, this was the next best option within my budget. The rooms were clean and private, located at a building on its own with only a few rooms. It's not in Vieux Quebec itself though but you can get there within 10mins of bus ride. Serge (the owner) is very helpful with travel information so don't hesistate to ask him ;)