My wife and I vacationed in Quebec City last October, and stayed on the Ile d'Orleans (about 20 miles away). We had no trouble finding short-term street parking in town; there is limited curb space near the Chateau Frontenac, right in the middle of everything. But I believe the street parking is restricted to 2 hours during the day.

The second day, we were in town all day so paid $13 (IIRC) to park in a private lot right off of Rue St. Louis.

You could also consider taking cabs and/or RTC buses instead of driving. I noticed taxi stands everywhere in Old Quebec (just as many as in Montreal, it seemed!)