You will be here right during the best of the fall colours, you should try to get to see them; however, half a day will not be enough! You will probably want to mostly wander in the Old-city. There are several museum in this area that you can visit (Musée de la Civilisation, Musée de l'Amérique Française). You could also take the ferry to get a nice view of the Terasse Dufferin and the Château Frontenac. You could visit the Citadelle and its surrounding, and also go to the plains of Abraham.

go to the old town in front of the Fontanbleu hotel and just walk the city walls and shops.

I second Patrick. Basically you'll want to spend your time just wondering the old city. He covered all the top spots. Have a blast!

There is no question that The old city is a must see especially the citadel and the plains of abraham. I'd make sure to run out and see Mont Morrency falls too though. You'll get some color on the way there and the view as it falls to the seaway is breath taking on a clear day.