I thought I would share some photos and thoughts about the (relatively) new Four Points property in Lévis, just across the St. Lawrence river from Quebec City. If you actually want to be in the dead center of Quebec City, it would not be a convenient property. However, if you have a car and are willing to drive to the ferry terminal in Lévis (about 2mi or so from the hotel), it is fairly convenient. The ride over on the ferry also offers an excellent view of Quebec City and the Chateau Frontenac.
We stayed in early January, so the temperature was a bit on the cold side. I don't believe it ever got above about 5F for the days we were there. The hotel itself was one of the new-style Four Points, with a well-appointed lobby/bar area and nicely furnished rooms. We were upgraded for the duration of our stay to an Executive Suite, which was one of the nicer Four Points rooms I've had. It actually reminded me of the suites I generally get at the Westin DFW. One interesting feature was the sliding wood partition between the living room and bathroom.
Below are some photos of the hotel and our suite:

Hotel Exterior (Taken from atop a 20ft high pile of snow at 5 below)

Executive Suite Entry/Kitchenette

Executive Suite Living Room

Executive Suite Living Room

Executive Suite Bedroom

Executive Suite Bedroom

Executive Suite Bathroom (Viewed through sliding partition from Living Room)

Executive Suite Walk-In Shower

Executive Suite Vanity

Executive Suite Soaking Tub

View From Top Floor (Chateau Frontenac can be seen near top-right)