During every day of the week - except, perhaps, on Sunday, that the thing is rather dead throughout the city - the historic center is a constant hotbed of people. But do not think that they are all guiris going from here to there looking at the pediments and domes of the churches to exclaim Oh my goddd and then point them with their digital cameras. No, the truth is that Quito - like the rest of Ecuador - is not too much exploited by tourism and you will see many more locals than foreigners in its streets.
The visit to the center can easily take you a whole day since - although it is not very large - the altitude at which the city is located will make you stop to take a breath every few times, being also its beautiful squares a good claim to sit to take some sun and eat something. I advise you to take some natural juices of a business that is going down one of the streets that leaves the Plaza de San Francisco. They only cost about 70 cents and are tremendous.