Where exactly is the parking? Someone mentioned it is at an hotel nearby, but not the name of the hotel. Is Parking D'Youville close enough in price to park there instead?
There is some parking on the street but Le Petit Hotel is a good place to park and not far away. You turn right immediately after coming out of the hotel and down a small street that is the distance of the length of the hotel and another behind, cross the road and Le Petit Hotel is the second down on the right. The parking lot is just below the hotel. These hotels are small, boutique type. If you can arrange parking at Le Petit Hotel before hand it may be the best way to go. As others have said there isn't a lot of parking, but the staff at the hotel are very helpful and will give you the best advice. We had no problems and were there at a relatively busy time. Once you're parked you'll probably spend your days walking through Old Quebec City, it is a close knit area and easy to get around on foot.
I think it was called Le Petit Hotel and it is very close, parking can be tight though. Sorry I don't know where the Parking you mentioned is. You can drop bags off outside the auberge easily.
Get an answer from Auberge La Chouette staff and past guests.