One of my favourite activities while in Quebec City is to spend an afternoon strolling through the old city. Be sure to bring a good pair of sneakers-- these roads have never been paved and feature the same cobblestones that our ancestors walked over 200 years ago!
You will know how to find the old part of the city by its most prominent building, the Chateau Frontenac. Although many believe that it was built as a residence, it was actually built for the purpose of being a hotel, which at five-stars is quite impressive. Frontenac is probably the most photographed building in the city, and its peaks and turrets are visible from almost any part of the city.
Scattered under the Chateau are many little buildings that are home to many little stores and boutiques. From antiques and tourist souvenirs to drugstores and even McDonalds, Old Quebec has everything.
If walking tires you out, catch a ride on one of the rickshaws, a human-drawn carriage. These boys are usually only available in the spring/summer months, and are usually university students who make this their summer job! I found that they knew alot about the old town, and were almost more knowledgeable than the hired tour guides!
There is a really awesome restaurant in the old part of the city called the 37th Parallel, which is supposedly right on the parallel line. Stop for a photo opportunity at their road sign which will tell you exactly how many miles away you are from Beijing, or Antarctica.
The old city has four different entrances, called "ports" and they are made of stone. The main entrance is called Port St Jean, because it opens onto Rue St Jean. If there is any kind of parade, be it a holiday or just a simple protest, you can be sure to view it by standing on this road. Rue St Jean is also the best road to find all your tourist shops, although beware of street beggars.
One more thing before I end this. At the very entrance to Port St Jean on the right, you will find a pavilion. In the winter, this transforms into a skating rink, with skate rentals and everything. There are also bleacher style benches to relax and watch the busy comings and goings. In the summer, these bleachers and pavilions are filled with street musicians playing bongoes and African drums. If you are looking for culture, don't pass by the pavilion!
Old Quebec is the oldest, and my most favourite part of the city. I don't think I would feel complete going to Quebec without stopping here.